Question

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

(Show work please)​

Answer 1

9
`√(2)` inches

or

12.728 inches

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

`(2a^(2) )/(2) =(324)/(2)`

Simplify

`a^(2) = 162`

Find the square root of both sides

`\sqrt{a^(2) } =√(162)`

a = 9
`√(2)`

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