Question

An equilateral triangle has an altitude of 21 inches. What is the side

length of the triangle?

14 2

7 2

7 3

14 3

Answer 1

7
`√(3)`

Explanation:

the altitude creates two congruent 30-60-90° triangles

the ratio of the sides in a 30-60-90°, respectively, are 1 :
`√(3)` : 2

therefore we can set up a proportion to find the side length:

let 'x' = side length of equilateral Δ

`√(3)` / 1 = 21 / x

cross-multiply:

`√(3)`x = 21

x = 21 /
`√(3)`

rationalize the denominator by multiplying numerator and denominator by
`√(3)`

21
`√(3)` /
`√(3)`·
`√(3)` = 21
`√(3)` / 3 or 7
`√(3)`