# What is the length of the side of a square whose diagonal is 10?

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#### Explanation

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#### Explanation:

I want someone to double check my answer

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Apr 13, 2016

Draw a diagram to represent your situation.

#### Explanation:

Since we're dealing with a square, all side lengths measure the same thing. Furthermore, the angle B and D are right, therefore allowing us to use pythagorean theorem to find the value of a.

color(blue)(a^2 + b^2 = c^2

Where $a \mathmr{and} b$ are the right containing sides

Since $a \mathmr{and} b$ are equal,we consider them as $a$

$c$ is the Hypotenuse of the right-triangle

The diagonal is the Hypotenuse $c$

$\rightarrow {a}^{2} + {a}^{2} = {10}^{2}$

$\rightarrow 2 {a}^{2} = 100$

$\rightarrow {a}^{2} = 50$

$\rightarrow a = \sqrt{50}$

color(green)(rArra=sqrt(25*2)=5sqrt2

So, the side lengths measure $5 \sqrt{2} \mathmr{and} 7.07$ units each.

Hopefully this helps!

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