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### 10 Square Units on Dot Paper

```Date: 03/01/2003 at 09:55:06
From: Cleonatra
Subject: Square units

How can I draw a square with 10 square units on dot paper?

Every time I try I can't seem to come up with a square with 10 square
units - only 9.
```

```
Date: 03/01/2003 at 11:50:05
From: Doctor Douglas
Subject: Re: Square units

Hi Cleonatra,

Thanks for submitting your question to the Math Forum.

To draw a square whose area is 10 sq units, the side length must
be sqrt(10) units long.  This means that the sides must be some
sort of diagonal line on the graph paper.

X   .   B   .     the square ABCD has sides of length
sqrt(1x1 + 2x2) = sqrt(5), so that its
A   .   .   .     area is 5 sq units.  We can see this
by applying the Pythagorean theorem to
.   .   .   C     the triangle AXB (we see that X is a
right angle)
.   D   .   .

So for a square whose area is 10 sq units, you'll need to find
a way to get a side of length sqrt(10).  Hint:  10 = 9 + 1.

Can you finish off the problem with this hint?

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Coordinate Plane Geometry
High School Puzzles
Middle School Puzzles

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