# 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?

Jan 12, 2017

The length of a side is $9 c m$. The length of the diagonal is $12.73 c m$.

#### Explanation:

The formula for area of a square is:

${s}^{2} = A$ where A=area and s=length of a side.

Hence:

${s}^{2} = 81$

$s = \sqrt{81}$

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.

${d}^{2} = {9}^{2} + {9}^{2}$

${d}^{2} = 81 + 81$

${d}^{2} = 162$

$d = \sqrt{162}$

$d = 12.73$