The altitude of an equilateral triangle is 12. What is the length of a side and what is the area of the triangle?

1 Answer
Dec 9, 2015

Length of one side is 8sqrt3 and area is 48sqrt3.

Explanation:

Let side length, altitude (height), and area be s, h, and A respectively.

color(white)(xx)h=sqrt3s/2

=>s*sqrt3/2color(red)(*2/sqrt3)=12color(red)(*2/sqrt3)
=>s=12*2/sqrt3color(blue)(*sqrt3/sqrt3)
color(white)(xxx)=8sqrt3

color(white)(xx)A=ah/2
color(white)(xxx)=8sqrt3*12/2
color(white)(xxx)=48sqrt3