Question

1. find the diagonal of a square with a perimeter of 20 inches.

Explanation:

Step1: Find side - length of the square

The perimeter formula of a square is $P = 4s$, where $P$ is the perimeter and $s$ is the side - length. Given $P=20$ inches, then $s=\frac{P}{4}=\frac{20}{4}=5$ inches.

Step2: Find the diagonal of the square

For a square of side - length $s$, the diagonal $d$ can be found using the Pythagorean theorem. In a square, if the side - length is $s$, then $d^{2}=s^{2}+s^{2}$ (since the two sides of the right - triangle formed by the diagonal and two sides of the square are of length $s$). Substituting $s = 5$ inches, we get $d^{2}=5^{2}+5^{2}=25 + 25=50$. Then $d=\sqrt{50}=5\sqrt{2}$ inches.

Answer:

$5\sqrt{2}$ inches