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

Answer:

$12\sqrt{2}\ cm$

Step-by-step 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

$d=\sqrt{288}\ cm$

simplify

$d=12\sqrt{2}\ cm$