Question

a square has a perimeter of 48 meters. what is the length of a diagonal?
12√3
6
24
12√2
question 5

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 $P = 48$ meters, then $4s=48$, so $s=\frac{48}{4}=12$ meters.

Step2: Use Pythagorean theorem for diagonal

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 the two sides of the right - triangle formed by the diagonal and two sides of the square are of length $s$). Substituting $s = 12$ meters, we get $d^{2}=12^{2}+12^{2}=144 + 144=288$. Then $d=\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}$ meters.

Answer:

D. $12\sqrt{2}$