Question

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

Answer 1

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`