Question

question 13 of 25
what is the length of side s of the square shown below?
a. $sqrt{2}$
b. 2
c. 1
d. 4
e. $4sqrt{2}$
f. $2sqrt{2}$

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 have length $s$). Given $d = 2$, we have $2^{2}=s^{2}+s^{2}$.

Step2: Simplify the equation

$4 = 2s^{2}$.

Step3: Solve for $s$

Divide both sides of the equation $4 = 2s^{2}$ by 2: $\frac{4}{2}=s^{2}$, so $s^{2}=2$. Then take the square root of both sides: $s=\sqrt{2}$ (we take the positive value since length cannot be negative).

Answer:

A. $\sqrt{2}$