# Thread:

1. ## Divided square

Hey guys i found a problem in the MENSA book, i've tried to use basic algebra to this this problem but i think i'm on the wrong track.
Can anyone suggest any techniques to do this problem?

The answers are at the back of the book although i do want to know how to do it.

THE IMAGE IS ATTACHED.

This field measures 177m x 176m. It has been split up into 11 squares that exactly equal the total area. The squares are only roughly drawn to scale. All new squares are in whole yards. Can you calculate the size of each square ?

- much appreciated.
Attached Thumbnails

2. It's a question of setting up the right system of equations. At least, that's how I solved it. Let each variable name be the length of a side of the corresponding square. Then the equations I have are the following:

$A+B=177$

$A+D=176$

$C+F=B$

$E+G=D$

$I+K=F$

$J+H=G$

$B+F+K=176$

$K+J+G+D=177$

$H+I=J$

$D+E+F=177$

$A+C+F=177$

$D=J+H+E$

$B+C+E+G=176$

At this point, admitting laziness, I turned the solution over to Mathematica, which spit out the result:

Spoiler:

A=99, B=78, C=21, D=77, E=43, F=57, G=34, H=9, I=16, J=25, K=41.

In principle, though, you would probably employ Gaussian elimination with back substitution to solve the system. You have a decently sparse system there, so it might not be all that messy, actually.

Cheers.

3. Thank you.

4. You're very welcome. Have a good one!

5. To mention, Beiler covers this type of problem in his book on number theory recreations.
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