Question

what is the length of side s of the square shown below? a. $sqrt{8}$ b. 1 c. $8sqrt{2}$ d. 4 e. $4sqrt{2}$ f. 2

Explanation:

Step1: Recall Pythagorean theorem for square

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

Step2: Solve for $s$

We have $8^{2}=2s^{2}$, so $64 = 2s^{2}$. Then $s^{2}=\frac{64}{2}=32$. Taking the square - root of both sides, $s=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

E. $4\sqrt{2}$