Challenging perimeter problem | Perimeter, area, and volume | Geometry | Khan Academy

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Perimeter of rectangle covered by 9 non-overlapping squares. From 2000 American Invitational Math Exam
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[@6freddyb]

@A010795 then their common divisor would be 2, W=122 - L=138. When the common divisor is 1, it's like asking what is the smallest sides can this rectangle be with the same proportions.

[@6freddyb]

@A010795 Right, think of it as fraction. If we place 122 and 138 over 1, we can reduced them by 2, so there common divisor is 2. Another example is on from the addition of fractions, let x=3, then y=6/5. The only common divisor they have in common is 5.

[@Noblyuntruthful]

Reminds me of a stoichiometric problem in chemistry.

[@HandsomeDevil456]

It's amazing how with only the given information, we can find out the exact dimensions of the rectangle

[@usmansharifmicky]

So you just guessed it would be 2 and 5, hmm. Honestly, isn't there a better way?

[@HandsomeDevil456]

I solved this on my own! But I spent way too long stuck at the end because for some reason I kept thinking the question's wording meant the length and the width had to be prime numbers. Of course when you solve it, you make it look like a piece of cake.

[@ggmm117]

This is awesome. Thanks

[@A010795]

What if you choose y to be 10 instead of 5?

[@austingubbels]

33 x 37 are also possible lengths/ widths if you do the problem a bit differently

[@127rajiv]

The interesting follow up is to add up the area of all the squares which should equal the area of the rectangle. 4209 .......

[@ilikechess1]

beautifully done. Great.

[@agronbandicoot]

please make a video about the kissing number problem sal!

[@laurabraga2758]

oh, ok, got it.

[@kazimrahman7499]

WoW....Lots a FUN.....how solve reveals by itself...!!

[@A010795]

@6freddyb ohh so no matter which integers you choose, you want the final answers to have a common divisor of 1?

[@hedonism13]

I hate myself for watching this. It would have been fun to find out for myself.

[@litterbox019]

9:03 *VERY NICE*

[@A010795]

@usmansharifmicky I asked the same question; but think about this. If you chose 10 and 4, the final answers would be divisible by 2, and the question asks for both numbers to have a common divisor of 1. So to answer the question properly you would still have to divide your numbers by 2 to get the same answer that you would get for 5 and 2.

[@Ashutosh-lj4ue]

A010795 jxjjnxjnxk shamanistic

[@Sam.Connon]

If you solve that x=2/5y, then can't you substitute 2/5y in for x in the equation 13x+7y=8x+9y? I got that x=2/5 and y=1, then subtituted both of those in each of the equations of the sides, and i got that the perimeter was 54. Did anyone else get that?

[@metaldave08096]

i figured most of it out myself, i just waited till he got started then went off on my own. It wasn't that hard.

[@jemappellelanoosh1743]

Can u do more of these challenging problems ?? They're amazing !

[@Hippoman141]

1337th view. This video is amazing

[@gkinfinityMelee]

Huh, that was pretty interesting

[@laurabraga2758]

Why Y is 5? I stopped in "pick a number time"

[@morgard211]

x = 2/5 • y is enough of a constraint to give us a concrete solution since the greatest common divisor is 1. Had he picked any other number, he would get the same result by simplifying.

[@MohamedGaber111]

very nice

[@symbolicmeta1942]

.....but why did you choose to plug 5 in? You could have plugged anything else in....and might have had to guess for ages...

[@jamjamw2972]

cool!

[@abhishekpandey9049]

still confused .....can anybody help ??????

[@Buoy2]

*non-overlapping

[@imranshalabi4373]

why is Y 5? and x 2

[@ishaniraj151]

such easy questions appear in American mathematics aptitude exams? That's why the intelligence level of Indian students is far ahead as compared to American students.

[@awesomecooly123]

You do realize that it says 2000 right? And you commented in 2014. 14 years man that's a lot of time for mathematics and society to advance.

[@bslate07]

That's why India is so far ahead of the United States in every way...Oh wait.

[@probablynotsatanic66]

Is that why USA always outperforms India at the annual IMO? Also, here are the rest of the problems on that year's AIME. Not many people can solve them. http:/www.artofproblemsolving.com/Wiki/index.php/2000_AIME_I_Problems