Five Equal Pieces of a Square Cake

Date: 05/22/2001 at 05:38:00
From: Katie
Subject: Maths challenge problem

Ravina has a square birthday cake. Its side length is 20cm. She wishes 
to cut the cake into five pieces, one for each of her four friends and 
one for herself. She wants to use straight vertical cuts to make five 
pieces of equal volume.

Suppose that Ravina makes the first cut from the cake's center to a 
point from the top left corner. Where must she make the other four 
cuts if they all start for the cake's center?

I haven't even started... I would not even know where to start.
Please help me!

Date: 05/22/2001 at 12:24:52
From: Doctor Peterson
Subject: Re: Maths challenge problem

Hi, Katie.

A good place to start is to think about what the area will be for any 
wedge cut from the cake, like this:

     +-----------+
     |           |
     |           |
     |     +     |
     |   /  \    |
     | /     \   |
     +--------+--+
     |<---d-->|

Once you've done that, think about the area of a wedge that goes 
around a corner, like this:

     +-----------+
     |           |
     |           |
     |     +__   |
     |   /    \  |
     | /       --+ --
     +-----------+  ^
     |<-------d-----+

You will find that the distance d along the outside is all you need to 
know, and using that you can find the correct value of d for which 
each piece is 1/5 of the cake. The answer is surprisingly simple!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/