Question

question 19 of 25 what is the length of side s of the square shown below? a. $sqrt{8}$ b. $4sqrt{2}$ c. $8sqrt{2}$ d. 2 e. 1 f. 4

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 $d^{2}=s^{2}+s^{2}=2s^{2}$.

Step2: Substitute the value of the diagonal

Given that the diagonal $d = 8$. So, $8^{2}=2s^{2}$, which simplifies to $64 = 2s^{2}$.

Step3: Solve for $s$

First, divide both sides of the equation $64 = 2s^{2}$ by 2: $\frac{64}{2}=s^{2}$, so $s^{2}=32$. Then, take the square - root of both sides: $s=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

B. $4\sqrt{2}$