There are two solutions because the image was not drawn to scale unless the larger square must be on the right.
@jpolowin010 ай бұрын
I've pointed this kind of thing out before... the area is equal to (128/3)√3, but only _approximately_ equal to the decimal expansion of 73.9 .
@flash24g10 ай бұрын
My method was to call the square side lengths x and y, and from x + y = 40 (squaring both sides) and x^2 + y+2 = 832 derive xy = 384. Also, if you know that a 30-60-90 triangle has sides in the ratio 1 : √3 : 2 then it helps a lot.
@toninhorosa48495 ай бұрын
Fantastic solution! 👏👏👏👏👏
@ManjulaMathew-wb3zn9 ай бұрын
I also took x and y to be side lengths of squares and x
@Marcus-y1m6 ай бұрын
I really appreciate the channel
@Mascig8310 ай бұрын
Good morning from Brazil. I wish the person responsible for this channel a Merry Christmas and may he continue to provide us with a wealth of knowledge in Mathematics❤.
@PreMath10 ай бұрын
Thanks dear ❤🌹
@ManjulaMathew-wb3zn9 ай бұрын
I would really like to clarify why the smaller value for x is chosen. If you assumed the side length of large square to be x you end up with the same quadratic equation. So the roots of the equation are simply the side length of each square where small one being 16 and the large one being 24. When you add them the answer is 40.
@AmirgabYT21854 ай бұрын
S=128√3/3≈73,899≈73,9
@yalchingedikgedik800710 ай бұрын
Thanks Sir Thanks PreMath With glades ❤❤❤❤
@cyruschang190410 ай бұрын
small square side length = a big squarebside length = b a^2 + b^2 = 832 a + b = 40 => a^2 + 2ab + b^2 = 1600 2ab = 1600 - 832 = 768 ab = 384 a + b = a + 384/a = 40 a^2 - 40a + 384 = 0 (a - 16)(a - 24) = 0 a = 16, b = 24 area = (16) (16/✓3)/2 = 8(16/✓3) = 128/✓3 = (128✓3)/3
@PreMath10 ай бұрын
Thanks❤
@cyruschang190410 ай бұрын
@@PreMath Happy holidays🎄🌟🎉🎆🥂
@PreMath10 ай бұрын
@@cyruschang1904 Happy and safe holidays as well ❤ Stay blessed 😀
@MrPaulc22210 ай бұрын
Okay, two different-sized squares that total 832cm^2, and a 30-60-90 triangle whose middle-length side is the same length as a side of the smaller square. Large square sides are a. Smaller square sides are b. Triangle sides are b, b/sqrt(3), and 2b (due to properties of 30-60-90 triangle). Maybe a simultaneous equation can sort this out: a + b = 40 (equation 1) a^2 + b^2 = 832 (equation 2). Rearrange 1: 40-b=a Substitute into 2: (40-b)^2 + b^2=832 1600-80b+b^2+b^2=832 2b^2-80b+1600=832 so b^2-40b+800=416so b^2-40b+384=0 Quadratic formula: (40+or-sqrt(1600-4*384))/2 = b (40+or-sqrt(64))/2 = b (40+or-8)/2 = b, so b = 24 or 16 24 and 16 are the squares' side lengths. b is earlier designated as the smaller square's sides. b=16, so the two sides of the triangle at right angles to each other are 16 and 16/sqrt(3). (8*16)/sqrt(3) is the area, but this can be tidied up. 128/sqrt(3) is equivalent to (128*sqrt(3))/3. The triangle's area is (128*sqrt(3))/3 cm^2. A close decimal is 73.9 cm^2. Just watched the video. The number manipulation used broadly similar methods though a bit different but, as expected, ended up with the same answers. My ways are a bit more circuitous because I have fewer tools and have to rely on the ones I've learned.
@PreMath10 ай бұрын
Thanks ❤️
@alster72410 ай бұрын
Merry Christmas, PreMath friends! 🌲🌲🌲🌲🌲🌲🌲☃️☃️☃️☃️☃️☃️🎅🎅🎅🎅🎅🎅 Also, in the step of finding the sides of the yellow ∆, the fastest way is to use the basic 30-60-90 properties. Since a= 16, we can solve for b by using a=b√3 16=b√3 16/√3 16/√3*(√3/√3) b= 16√3/3 units Then the rest are easy.
@PreMath10 ай бұрын
Thanks dear❤
@prossvay874410 ай бұрын
a is small square and b is big square a+b=40 ; a^2+b^2=832 a=16cm ; b=24cm Tan(60)=16/x x=16√3/3 Area of the yellow triangle=1/2(16)(16√3/3)=128√3/3=73.9cm^2. Thanks ❤❤❤
a^2+b^2=832, a+b=40, ab=(40^2-832)/2=384, a, b given by (40+ - 8)/2=16, 24, small square is 16×16, the width of triangle is 16/sqrt(3), the area=1/2 16×16/sqrt(3)=128/sqrt(3)=128/3 sqrt(3).😊
@PreMath10 ай бұрын
Many many thanks❤
@devondevon436610 ай бұрын
73.9 128/3 (sqrt 3) or 73.9 Let area of the small square = 'a' and area of large = 'b', then a^2 + b^2 = 832 Equation 1 a + b = 40 Hence, a = 40 - b Equation 3 Hence (40-b)^2 + b^2 = 832 ( substitute Equation 3 into Equation 1) 1600+ b^2 -80b + b^2 = 832 2b^2 - 80b + 768 =0 b^2 - 40b + 384 =0 (divide by 2) (b-16) (b-24) = 0 b= 16 and b= 24 Hence the side of the small square = 16 and large = 24 Since it faces a 60 degree right triangle then 16 = x sqrt 3 and the other leg = x x = 16/sqrt 3 = (16 sqrt 3)/3 Hence area = (16 sqrt 3)/3 * 16 * 1/2 = 128/3 (sqrt 3 73.9 square unit
@PreMath10 ай бұрын
Thanks❤🌹
@phungpham172510 ай бұрын
Thank you so much! It is a lot of fun solving this problem! The picture looks like a truck pulling 2 squares. Label the sides of the squares as a and b and assume that a a= 16 Because the yellow triangle is a special 30-90-60 one of which the height = a =16 so its base= 16/sqrt3 The area= 1/2 . 16/sqrt3 .16= 73.9 sq units
@PreMath10 ай бұрын
Thanks❤
@safanaazadworld10 ай бұрын
Good
@PreMath10 ай бұрын
Thanks❤️
@wackojacko396210 ай бұрын
@ 8:28 , ... knowing 30-60-90 triangle rules you can save a lot of time and energy just knowing the (adj-side) × 3½ = 16. Solve for (adj-side) ,Then rationalize and wallah, base times height equals area! 🙂
@PreMath10 ай бұрын
Thanks❤
@flash24g10 ай бұрын
Where do you get 3½ from?
@Kero-zc5tc10 ай бұрын
Could you solve this by doing a2+b2=832 then doing a2=832/b2 and rearranging to get quadratic formula but with (x2-1) instead of (x-1)?
@Alishbafamilyvlogs-bm4ip10 ай бұрын
So beautiful so nice and good work may Allah bless you stay connected🎉🎉🎉❤
@PreMath10 ай бұрын
Thanks❤
@RobG172910 ай бұрын
x = 24 won't work as that is more than half of 40, and it is the smaller square's side. The ratios of sides in a 30 60 90 right triangle would be enough to calculate the length of the smallest side.
@PreMath10 ай бұрын
Thanks❤
@prossvay874410 ай бұрын
Tanks teacher ❤❤❤
@PreMath10 ай бұрын
Always welcome ❤️🇺🇸
@himo348510 ай бұрын
x^2+(40-x)^2=832 2x^2-80x+1600=832 2x^2-80x+768=0 x^2-40x+384=0 (x-16)(x-24)=0 x
@PreMath10 ай бұрын
Many many thanks❤
@Mascig8310 ай бұрын
Please clarify two doubts for me: 1) How was the number 384 divided to result in 16 and 24? 2)When calculating the area, how did 128 come about?
@Mascig8310 ай бұрын
@@GordonSimpson-hr4yf Good morning Mr. Gordon. Thank you for answering my question. If it doesn't bother you, please explain to me something else: I factored 384 and the result was this: the number 2 multiplied 8 times and by 3.
@Mascig8310 ай бұрын
Good morning, Mr. Gordon, how are you? When I factored the number 384, it resulted in 2⁷ x3. Again bothering you, please show me the calculations you performed to find those two numbers, 24 e 16.
@Mascig8310 ай бұрын
Good afternoon, Mr. Gordon. Thank you so much for this precious and undoubtedly comprehensible explanation ❤ You should create a You Tube channel on Maths🙂📚📚📚
@mathswan160710 ай бұрын
128/3*sqrt(3)
@EmmanuelGiouvanopoulos10 ай бұрын
Merry Christmas man
@PreMath10 ай бұрын
Same to you! Thanks❤
@Kambyday10 ай бұрын
Let x be side of smaller square x + y =40 y=40 -x x² + y² =832 x² + (40-x)² =832 x² +1600 +x² -80x =832 2x²-80x+768=0 x²-40x+386=0 x=20±√14 y=20±√14 Assuming x
@PreMath10 ай бұрын
Thanks❤
@Kambyday10 ай бұрын
@@PreMath why is my answer wrong can you explain?
@rajendraameta799310 ай бұрын
24 is rejected ?
@delfyruiz744410 ай бұрын
How , or where is the 80x come from
@PreMath10 ай бұрын
Hello dear, we used the identity! Thanks❤
@JSSTyger10 ай бұрын
Ok i tried it all in my head. I believe the answer is 128/sqrt(3).
@JSSTyger10 ай бұрын
The squares are 24 by 24 and 16 by 16. The triangle has legs of 16 and 16/sqrt(3).
@nunoalexandre640810 ай бұрын
Solve it in less than 5 minutes!!!!!
@DB-lg5sq10 ай бұрын
شكرا لكم ينبغي زيادة xاصغر من 40 ناقص x
@PreMath10 ай бұрын
Thanks❤
@aka_vitfil10 ай бұрын
23 seconds and... DONE!
@PreMath10 ай бұрын
Thanks❤
@terrybaileysr.371410 ай бұрын
This is not right. The two squares are not the only area. There is a section between the two squares you did not account for. If I was buying carpet for those two rooms I would come up short. You left out the part in the doorway.
@bruuuuuh84110 ай бұрын
free palestine😢
@PreMath10 ай бұрын
☮️
@anime_lover1237910 ай бұрын
Why you people insert geo politics in every field can't you stay in peace