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### 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.
```

```
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/
```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Higher-Dimensional Geometry
Middle School Triangles and Other Polygons

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