Question

The area of a square is 144 square centimeters. Find the length of the diagonal. Write your answer in simplest radical form.

Answer 1

`12√(2)\ cm`

Explanation:

step 1

Find the length side of the square

we know that

The area of a square is equal to

`A=b^(2)`

where

b is the length side

we have

`A=144\ cm^2`

substitute in the formula of area

`144=b^(2)`

solve for b

square root both sides

`b=12\ cm`

step 2

Find the length of the diagonal

Applying the Pythagorean Theorem

`d^2=b^2+b^2`

see the attached figure to better understand the problem

substitute the given values

`d^2=12^2+12^2`

`d^2=288`

square root both sides

`d=√(288)\ cm`

simplify

`d=12√(2)\ cm`