/sci/ - Science & Math

bump, I really want an answer

let's go, work your brains.

I'll go with the bet that this isn't homework (could be some extra credit thing, though, I guess).

It's probably not the best way to solve this, but I think you can do something by noticing that the 4 right triangles are similar triangles. If you write <span class="math">a[/spoiler] the horizontal side of the top left triangle, <span class="math">b[/spoiler] its vertical side and <span class="math">c[/spoiler] its hypotenuse, and <span class="math">a'[/spoiler], <span class="math">b'[/spoiler] and <span class="math">c'[/spoiler] the matching sides on one of the small triangles, then you have:
<span class="math">a+b'=5[/spoiler]
<span class="math">b'+a=13[/spoiler]
<span class="math">c'=1[/spoiler]
<span class="math">\frac{a'}{a}=\frac{b'}{b}=\frac{c'}{c}[/spoiler]

You're looking for <span class="math">c[/spoiler], and the remainder is boring algebra.

>>4339260
c would be the hypotenuse of the entire room if you split it into two triangles, we're looking for the length of the carpet, it is not the same.

>>4339260
Actually I'm missing something, am I not?

>>4339262
No I'm talking about the 4 triangles around the carpet. I'm too lazy to draw that, be <span class="math">c[/spoiler] is the side of the carpet.

(5 - x) * (13 - y) + xy + z = 65
z² = (13 - y)² + (5 - x)²
x² + y² = 1

http://www.wolframalpha.com/input/?i=%285+-+x%29+*+%2813+-+y%29+%2B+xy+%2B+z+%3D+65%2C+z%C2%B2+%3D+%
2813+-+y%29%C2%B2+%2B+%285+-+x%29%C2%B2%2C+x%C2%B2+%2B+y%C2%B2+%3D+1

z= 13.3258

>>4339266
Beautiful, thanks!

>>4339266
though I get z = sqrt(193) which is 13.9

>>4339270
Wolfram probably solved this numerically. That happens with systems of non-linear equations.

>>4339270
nvm, I made a mistake...

>>4339271
Huh I didn't notice there was such a big difference. I withdraw my comment about numerically solving this, I doubt it would create such a big discrepancy.

>>4339273
no, Wolfram probably did it correctly. I made a mistake in my calculations... I put (5-x)^2 as 25-x^2 when it's actually 25-10x+x^2

>>4339266
Fantastic.