Question

The height of the equilateral triangle below is 15 units. What is the value of x?

Answer 1

Step-by-step explanation:

The height of the equilateral triangle below is 15 units

Let x is the side of the equilateral triangle

Equilateral triangle is divided into to two special right triangles 30-60-90 degree triangles

Height is 15 units

Hypotenuse is x

use the general ratio of  30-60-90

compare the sides and find out hypotenuse x

$a\sqrt{3} =15\\\\\frac{a\sqrt{3}}{\sqrt{3} } =\frac{15}{\sqrt{3} } \\a=\frac{15}{\sqrt{3} }$

now replace the value of 'a' for x=2a

$x=2a\\x=2 \cdot \frac{15}{\sqrt{3} } \\x=2 \cdot \frac{15\sqrt{3}}{3} \\\\x= 10\sqrt{3}$

Answer:

$x= 10\sqrt{3}$