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leva [86]
3 years ago
10

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

Mathematics
1 answer:
maks197457 [2]3 years ago
3 0

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

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