The area of a square is 81 square centimeters. First, how do you find the length of a side Then find the length of the diagonal?

1 Answer
Suren Abreu
Jan 12, 2017

The length of a side is #9cm#. The length of the diagonal is #12.73cm#.

Explanation:

The formula for area of a square is:

#s^2=A# where A=area and s=length of a side.

Hence:

#s^2=81#

#s=sqrt81#

Since #s# has to be a positive integer,

#s=9#

Since the diagonal of a square is the hypotenuse of a right-angled triangle formed by two adjacent sides, we can calculate the length of the diagonal using the Pythagorean Theorem:

#d^2=s^2+s^2# where d=length of the diagonal and s=length of a side.

#d^2=9^2+9^2#

#d^2=81+81#

#d^2=162#

#d=sqrt162#

#d=12.73#

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