A triangle has sides 10 and 6 - what could be the missing side?

How to find the side of a triangle using the triangle inequality. Learn more math at TCMathAcademy.com/.
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[@davethomson5921]

Unbelievably convoluted explanation. 10-6=4, but thats a straight line. So x>4 to form a triangle.

[@MarkTWirth]

How about the shortest distance between two points is a straight line? Anything less than 5 would make that statement fail.

[@PrithwirajSen-nj6qq]

Problem 1 The sum of two sides of triangle is greater than the third side. 10 + 6 =16 All the options satisfies the theorem. But all options are not right. Now we have to check with respect to the theorem below . Theorem --- The difference of two sides of a triangle is less than the third side. 10-6=4 Hence option 1/2/3 does not satisfy the theorem. 10-6

[@Vipre-]

Never heard of this before. Not sure when I'd use it but into the back pocket it goes.

[@craigsaunders7037]

My proof was, let angle opposite x=0, a straight line. X would = 4. As soon as angle opposite x>0 you have a triangle, but x is also going to be > 4. Therefore answer is 5.

[@stephena1196]

I was confused about this, as I generally assume one can't do it if you can't draw it with protractor, compass and ruler. Then I suddenly realised it must be five because if it was four it would be a straight line and any less the ends wouldn't join. A day without maths is like a day without sunshine.

[@larrystuder6378]

I learned something from this problem and your answer- it's not arithmetic, and it's not REALLY math, but looking at the problem with logic, your answer is absolutely correct and sensible. Anything shorter would not enclose the figure, or would make a single line. A worthwhile exercise.

[@randyfust2304]

I think you need an angle to solve.

[@larrystuder6378]

@@randyfust2304 that was my first thought. But since you don't have that, is there another way? And yes there is- with most of the possible answers, the 6 unit side and the suggested answer add up being shorter than the 10 unit side, so the figure CANNOT close, and one of them, the 6 and the 4, if you line them up as a single straight line, they exactly overlay the 10, making the exact same line, not a 2 dimensional figure..

[@briangallagher8444]

Your videos are a greT help, thank you so much. What if two of the answ options were greater than 5 ? Thanks

[@keithzinn457]

Great perspective(s) on this lesson. I've seen a few of your videos now and they are great at providing that. As with anything, there are multiple ways to come to a conclusion and you always provide some good OE with the solutions provided. Thank you!

[@pas6295]

Sum of the two sides of a triangle greater than the third side. It is a pirtulate

[@erembald2927]

It can only be 5 because 6 + any of the other values is les than or equal to 10 and a triangle would not be formed

[@IbrahimAdegbite-z7k]

Excellent! Never heard of the rule of Triangle Inequality before. Thanks for making my day.Will definitely teach my kids.

[@abdulqadersaidi7658]

Excellent explanation your method of teaching is really very professional , fantastic and enjoyable this particular problem makes me to understand the concept of triangle inequality which was forgotten long time ago. Highly appreciated. Thanks

[@stevenjohnson1143]

Using the Triangle inequality law the first three creates numbers less than or equal to 10 and since it must greater than 10 d 5 is right

[@motorbuzz4748]

You can't tell by the drawing the value of x, but you can certainly tell out of the choices which ones it isn't.

[@dogslife4831]

Loved this one ❤ Min > 4 and max < 16 4 & 16 are straight lines

[@InCognito-yq5ew]

TG I have AutoCAD and a angle finder because that was confusing AF.

[@argonwheatbelly637]

d. It's less a solve question and more of a test taking technique one. It DOES require you to think about what a triangle is. And that makes it a good question.

[@user-hr3fb5qw6d]

Get to the fuclin explanation- please!

[@duncan-rmi]

I looked at it & saw lines on a football pitch, A to B along the '10' side & A to B also along the '6' & 'x' sides with a little change of direction in the middle. if you ran those two paths, they'd take different amounts of time, so the total distance has to be greater than 10. only one answer makes that right.

[@josephlaura7387]

Thank you

[@user-ct8li9mi9k]

Thank you for that! I'm a little ashamed I never knew that.

[@edpottinger849]

In this case it's a little simpler because 6 + x= 10,there isn't two unknowns.The answer is c 4.Some of the other stuff you put on with 3 variables and no way to factor ate a lot harder.Thats what I need to learn more about.

[@francistorchio]

Basic properties of a triangle, to wit: the sum of any two sides of a triangle is always greater than the third side.

[@russelllomando8460]

got it D 5 sum of 2 sides must be greater than the 3rd thanks for the fun

[@stphinkle]

8 is another possible answer. 6^2 + 8^2 =10^2. 36+64=100. In fact, this could be a 3-4-5 triangle with the other numbers.

[@gavindeane3670]

Anything greater than 4 and less than 16 is a possible answer. This question works because it is presented with multiple choice answers, only one of which is possible.

[@keeganafrica7783]

Pythagoras only works with right triangles

[@richardhole8429]

A B and C fail to be triangles. X+6 must be greater than 10. Only D satisfies the problem.

[@robertstuart6645]

I presume the next step is to use the Law of Cosines to compute the angles in order to verify all of the lengths are valid.

[@petersearls4443]

My math is kind of rusty. Don’t cosines need an angle?

[@panlomito]

Rotate the 10 side over the left end of the line to the horizontal and you will know x must be larger than 4...

[@pas6295]

Portulate

[@devondevon4366]

5 since 6 + 5 = 11, which is greater than one of the side 10, the combined length of any of the two sides must be greater than the other side

[@viz8746]

Question should be made more challenging by lengthening the '6' line to give the optical illusion - anyone can tell it can only be 5 from the visual.

[@aydinorhan1]

Thank you very much for making me think I was very smart, even if only for a few seconds.

[@Christopherdpenha]

John the JACKASS who has a special quality, he always makes a mountain of a mole hill

[@leonidasvafiadis4635]

The sum of 2 sides of a triangle shoul be greater than the 3rd side. So 5.

[@gilmarjosedonascimentojose3480]

Como os desenhos não estão em escala, este tipo de questão fica muito aberto, pois , com certeza podemos ter valores de 1um, até 15 um.

[@amatasos7293]

To be accurate we have to get at least one angle value.

[@MrSummitville]

Umm, no ...

[@gavindeane3670]

No we don't. It's a multiple choice question and 3 of the 4 options for the answer fail to make a triangle.

[@MrSummitville]

@@gavindeane3670 Answers ... a) , b) and c) fail to make a triangle. The answer is d)

[@krisswegemer1163]

4 is possible with angles = to zero.

[@Vipre-]

But that wouldn't be a triangle, it'd be a line.

[@thenetsurferboy]

Why not just work it out using the formula? c^2 = a^2 + b^2 -2ab[cosine c] The letters correspond to the sides opposite the vertices

[@thenetsurferboy]

Sorry I forgot to solve the problem at hand

[@user-jo7db5xb8j]

Sum of two side is more than third ... So Answer is 5

[@arunsharma-lp4vx]

Surely the answer could also be 8 as it is a multiple of a pythagorean 345 triangle.

[@gavindeane3670]

8 is not one of the options. Any value greater than 4 and less than 16 is possible for x. This question only works because it's presented as multiple choice and only one of the options is possible.

[@nikolaysharapov6298]

5. Третья сторона не может быть равна и больше суммы двух сторон. И , не может быть меньше их разности и равна этой разности.

[@davidgagen9856]

Gee....cant be 2,3 or 4 cos that wd make the shortest dist between 2 points not a straight line.

[@markpoullos]

Wow, I am fairly proficient and trigonometry, but I have either never learned or heard of the triangle inequality. I did get the answer right. Go figure! Thanks again.

[@gavindeane3670]

I don't think I've ever heard it referred to as "the triangle inequality" before either. It is a statement of the blindingly obvious to note that if one side length of a triangle is X then the other two side lengths must add to more than X. I don't think we need to go through the bother of formalising something like that into a theorem with a name.

[@wataniarabi6095]

The wording is poor, because the size of X is related to the angle between the lines (10) and (6). From the figure, the correct answer would be 4

[@richardsmith3905]

4 by graphic solution

[@Surreal_Wizard]

If eight isnt one of the choices (because it's the most obvious answer) then it certainly can NOT be 4 or 5. Has to be either 2 or 3; more than likely 3. (Oops... :( Looks like Mr. KZbin Math Man got me on this one )

[@richardswenson4669]

5

[@samjones3106]

If your traveling at the speed of light a is correct.

[@MrMousley]

If one side is 10 and another side is 6 then the third side has to be more than 4 so 5 is the only possible answer.

[@th3dudeabides1]

Clearly this isn't drawn to scale. But it has to be 5. No other answer works

[@comdo777]

asnwer=(c)4 isit

[@donagregge8820]

3

[@user-jq4pn4cc1w]

My answer is 4

[@mvssarma3387]

It is 5

[@mr.howard3785]

Geometry is why I became an accountant and not an engineer.

[@richardhole8429]

I bet you are happy with that decision. The world could not function without accountants, a necessary and honorable career.

[@jhferu]

​@@richardhole8429accountancy is a great (and very popular) profession for people who aren't good at mathematics ;)

[@sekharb6651]

8

[@alaeddinemustapha8496]

5. 6+x>10

[@RamavtarAgrawal-r8f]

D 5

[@davemorley2367]

its not draw correctly, on my screen the ten measures 184mm and x measures 59mm

[@gavindeane3670]

It doesn't need to be drawn to scale. That's why the side lengths are given.

[@radicalrick9587]

*Let's break down the answer for those who wish to understand this type of theorem better.* To find the value of 𝑥 in the given triangle, we can use the properties of triangles. Given that the triangle has sides of length 10, 6, and 𝑥, we should check if it forms a right triangle. If it is a right triangle, the Pythagorean theorem will apply: a² + b² = c² If we assume 𝑥 is one of the legs and 10 is the hypotenuse, we should apply the Pythagorean theorem correctly: 10² = 6² + 𝑥 ² 100 = 36 + 𝑥 ² 100 - 36 = 𝑥 ² 64 = 𝑥 ² 𝑥 = √64 𝑥 = 8 Since this result is not one of the given options (2, 3, 4, 5), we'll use another configuration where 𝑥 is not the hypotenuse. Assuming the given triangle is not a right triangle, we will use the triangle inequality theorem: 1. 𝑥 + 6 ≻ 10 2. 𝑥 + 10 ≻ 6 3. 6 + 10 ≻ 𝑥 Solving these inequalities: 1. 𝑥 ≻ 4 2. 𝑥 ≻ -4 (always true for positive 𝑥) 3. 16 ≻ 𝑥 So, 4 ≺ 𝑥 ≺ 16. the only value among the given options that satisfies this range is: 𝑥 = 5 Therefore, the correct value for 𝑥 is 5.

[@user-pj9mi9rn4k]

Rubbish. X = 11.66? No, its 8. Hypo squared = squares of other two sides. I.e. x² = 100 - 36 = 64 X = 8.

[@radicalrick9587]

@@user-pj9mi9rn4k *My apology, you are correct. I should have double checked.* *Fixing it now.* *Thanks for pointing that out.*

[@user-pj9mi9rn4k]

@@radicalrick9587 Sorry about the 'rubbish'! Really should have been more polite!

[@radicalrick9587]

@@user-pj9mi9rn4k *We're only human, we all say or do things we wish we could take back.*

[@abrahammg9814]

5 correct answer

[@krishnaswamyv-nb5zh]

Confusing

[@parmitachoudhurychoudhury2734]

According to pythagoras theoram the ans is 8

[@gavindeane3670]

x only equals 8 if this is a right-angled triangle. The only thing we know from the diagram is that x must be greater than 4 and must be less than 16. Any other value for x is impossible because it would fail to make a triangle. Looking at the multiple choice options, the only answer it could be is 5. Note that this is another one where the question in the video description is worded differently to the question in the thumbnail image. The wording in the description is correct.

[@KundrawatiKundrawati]

x=3

[@darienchrysafis3655]

C

[@tinaterry1280]

❤❤❤❤❤❤

[@syedsharifuddinahmad2422]

5 6+x should be greater than 10

[@chrisdissanayake6979]

X = 5

[@Ayelmar]

Solved at the thumbnail, the only viable answer is d) 5. (Technically anything GREATER than 4 but less than 16.) An answer of 4 or 16 would result in the "triangle" jus tbeing a line, given the existing lengths of 10 and 6. Anything smaller than 4 or larger than 16 is impossilble, unless you're in a Lovecraftian, non-Euclidean nightmare world.... 😜

[@yanamadalabhanuraju6721]

D

[@PravinRathod-ee5ts]

Unnecessary made complicated and lengthy...

[@samuelpete]

A

[@christiesebaratnam9155]

The traingle can be drawn with any one of the answers

[@gavindeane3670]

No it can't. Answers a, b, and c do not make a triangle. x has to be greater than 4 and less than 16. Only answer d works.

[@KundrawatiKundrawati]

IM wrong 😅

[@peterthomas5792]

Sheesh! This a problem that takes longer to read than solve. Seriously?

[@TSR1942]

What is it you are telling? Absurd

[@user-pj9mi9rn4k]

Why does this guy always make a meal of it? If the angle was 0, then x would be 10 - 6 = 4. But it isn't 0, so it must be > than 4. Therefore 5. End of.

[@chrissullivan40]

Bad answer. We need a formula not a process of elimination.

[@gavindeane3670]

But elimination is exactly how you solve this. The answer is d because the other three options fail to make a triangle. If you want to formalise it, then 6 + x > 10 is the only formula we need.

[@soshakobyan3123]

Is this a joke?

[@timrocksnrolls]

Your explanation is far too complicated.

[@allenarbeau]

Dude. Just explain the solution for christ sake. You have a 10 minute video of blathering for a 10 second solution.

[@KM-gf8oy]

Terrible horrible ridiculously bad explanation. 5 is not the solution. 5 is A Possible Solution. There is a huge difference. The heading says "Which is correct" It doesn't say which one might be correct. If you can't even state the question properly how in the heck are you going to do a logical solution? A much better way to teach math is to help students understand the logical path to arrive at a solution. For example: 4 x Y = 8 what is Y? You can solve for Y and get 2. He uses the rather abstract triangle inequality rule without an explanation as to why it makes sense. This might be hard to visualize but picture the long leg rotating clockwise stretching the length x if you can visualize that you can see that x can be a lot of different values. If you rotate the long leg all the way clockwise and make the triangle almost flat x approaches 4. It could be 4.0001 and you still have a triangle. Rotate the long leg the other way counterclockwise as far as it'll go. You have another very flat triangle and you could get as close as you wanted to 16. For example 15.999. so the actual solution to the problem can be any number less than 16 and greater than 4. The instructor didn't help you visualize that process. This will only confuse students but how to solve triangle problems again terribly done.

[@gavindeane3670]

He has stated the question differently (and correctly) in the video description, but you're absolutely right about the thumbnail image - the question in the thumbnail image is worded incorrectly. Not the first time this has happened with his videos...

[@larryzimmer8739]

You need to go back to drawing class. The proportions of the drawing do not support the answer.

[@gavindeane3670]

There's no reason to expect a diagram in a question like this to be drawn to scale. Indeed, it can be a good thing if the diagram is purposely NOT drawn to scale.

[@josephlaura7387]

Thank you

[@ojaichuck]

5

[@johnmayer5920]

3

[@rodfulford4306]

D

[@user-ct4pi6rt2z]

5

[@user-kg1eo6xd8t]

4

[@mawavoy]

5

[@ebiebrahimian4248]

5

[@bevdavis8550]

4

[@Happy2beher]

D

[@Happy2beher]

The sum of any two sides of a triangle must be > than the largest side!!