# Interesting problem

• Apr 23rd 2013, 10:33 AM
aaronrpoole
Interesting problem
• Apr 23rd 2013, 12:53 PM
MarkFL
Re: Interesting problem
Can you find the diagonal using the law of cosines?
• Apr 23rd 2013, 03:55 PM
Soroban
Re: Interesting problem
Hello, aaronrpoole!

MartFL gave you a powerful hint.
But the answer is even simpler.

Consider the zigzag line.

Code:

      *       |.     3| .       |  . 4       *---.-----*       :  d.    |       :    .  |     5:      .  |5       :      . |       :        .|       * - - - - *           4
We want the hypotenuse $\displaystyle d$ of a 4-by-8 right triangle.

Then the side of the square is: $\displaystyle \frac{d}{\sqrt{2}}$

Therefore, the area of the square is: $\displaystyle \frac{d^2}{2}$
• Apr 23rd 2013, 07:54 PM
aaronrpoole
Re: Interesting problem
I'm pretty sure I'm supposed to have an integer value for the answer
• Apr 23rd 2013, 08:05 PM
MarkFL
Re: Interesting problem
Using soroban's technique, you will get an integer.
• Apr 23rd 2013, 09:33 PM
aaronrpoole
Re: Interesting problem
yeah I figured that out after I posted that. lol im stupid :p
Thanks for the help guys.