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: Recall Pythagorean theorem for square

Let the side - length of the square be $a$. In a square, if the diagonal is $d$, by the Pythagorean theorem $d^{2}=a^{2}+a^{2}=2a^{2}$ since the two sides of the right - triangle formed by the diagonal and two sides of the square are equal.

Step2: Substitute the given diagonal value

Given $d = 10$, we have $10^{2}=2a^{2}$, so $100 = 2a^{2}$.

Step3: Solve for $a$

First, divide both sides of the equation $100 = 2a^{2}$ by 2: $\frac{100}{2}=a^{2}$, which gives $a^{2}=50$. Then, take the square root of both sides: $a=\sqrt{50}$. Simplify $\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

E. $5\sqrt{2}$