Question

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?

Answer 1

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`