Divided square

• Jan 18th 2011, 10:41 PM
qwertyuiop
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. (Wink)
• Jan 19th 2011, 02:43 AM
Ackbeet
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.
• Jan 20th 2011, 07:27 AM
qwertyuiop
Thank you.
• Jan 20th 2011, 07:49 AM
Ackbeet
You're very welcome. Have a good one!
• Jan 20th 2011, 12:12 PM
wonderboy1953
To mention, Beiler covers this type of problem in his book on number theory recreations.