Question

what is the length of side s of the square shown below? a. 1 b. 4 c. 2 d. 2√2 e. 4√2 f. √2

Explanation:

Step1: Apply 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 in a right - triangle formed by two sides and the diagonal of the square, the two legs of the right - triangle have length $s$). Given $d = 2$, we have $2^{2}=s^{2}+s^{2}$.

Step2: Simplify the equation

$4 = 2s^{2}$.

Step3: Solve for $s^{2}$

Divide both sides of the equation $4 = 2s^{2}$ by 2, we get $s^{2}=2$.

Step4: Solve for $s$

Take the square root of both sides. Since $s>0$ (as it represents the length of a side of a square), $s=\sqrt{2}$.

Answer:

F. $\sqrt{2}$