Question

select the correct answer.
what is the height, x, of the equilateral triangle shown?
a. 5 in.
b. $5\sqrt{3}$ in.
c. 10 in.
d. $10\sqrt{3}$ in.

Explanation:

Step1: Split triangle into 2 right triangles

The base of each right triangle is $\frac{10}{2}=5$ in, hypotenuse = 10 in.

Step2: Apply Pythagorean theorem

Use $x^2 + 5^2 = 10^2$ to solve for $x$.
$x^2 = 10^2 - 5^2 = 100 - 25 = 75$

Step3: Solve for x

$x = \sqrt{75} = 5\sqrt{3}$

Answer:

B. $5\sqrt{3}$ in.