Question

a diagonal of a square measures 10 units. what is the length of one of its sides?
a. 5
b. 10
c. $\frac{5sqrt{2}}{2}$
d. $10sqrt{2}$
e. $5sqrt{2}$

Explanation:

Step1: Apply Pythagorean theorem

Let the side - length of the square be $a$. In a square, if the diagonal is $d$, by the Pythagorean theorem $d^{2}=a^{2}+a^{2}=2a^{2}$. Given $d = 10$, we have $10^{2}=2a^{2}$.

Step2: Solve for $a$

We get $100 = 2a^{2}$. Then $a^{2}=\frac{100}{2}=50$. Taking the square - root of both sides, $a=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

E. $5\sqrt{2}$