Question

find the length of the diagonal of a square with perimeter 32. p = 32 a. $4sqrt{2}$ b. 8 c. $2sqrt{2}$ d. 45 e. $8sqrt{2}$

Explanation:

Step1: Find side - length of square

The perimeter formula of a square is $P = 4s$, where $P$ is the perimeter and $s$ is the side - length. Given $P = 32$, then $4s=32$, so $s=\frac{32}{4}=8$.

Step2: Use Pythagorean theorem

In a square, if the side - length is $s$ and the diagonal is $d$, by the Pythagorean theorem $d^{2}=s^{2}+s^{2}$. Since $s = 8$, then $d^{2}=8^{2}+8^{2}=64 + 64=128$.

Step3: Solve for diagonal

$d=\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}$.

Answer:

E. $8\sqrt{2}$