Question

Given an equilateral triangle with side lengths 18 cm. What is the height of the triangle?

O 18 cm
O 9 cm
o 93 cm
O 183 cm

Answer 1

Explanation:

If you draw an altitude of the right triangle, you get that the legs are (18/2)=9 and the height (which I'll call x) and a hypotenuse of 18.

By the Pythagorean theorem,

`{9}^(2) + {x}^(2) = {18}^(2) \\ 81 + {x}^(2) = 324 \\ {x}^(2) = 243 \\ x = √(243) = 9 √(3)`