Question

A square has a diagonal length 18 in. What is the side length of the square?

Answer 1

Answer:

9$\sqrt{2}$ inches

or

12.728 inches

Step-by-step explanation:

Use Phytagorean Theorem

$a^{2} +b^{2} =c^{2}$

Since both all sides of a square are equal, this means that $a^{2}$ and $b^{2}$ are equal.

So that leaves us with:

$a^{2} +a^{2} = 18^{2}$

Simplify

$2a^{2} = 324$

Divide both sides by 2

$\frac{2a^{2} }{2} =\frac{324}{2}$

Simplify

$a^{2} = 162$

Find the square root of both sides

$\sqrt{a^{2} } =\sqrt{162}$

a = 9$\sqrt{2}$

(or if you want the decimal, rounded to the 3rd decimal place: 12.728)