Question

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

Answer 1

Answer:

7$\sqrt{3}$

Step-by-step explanation:

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

the ratio of the sides in a 30-60-90°, respectively, are 1 : $\sqrt{3}$ : 2

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

let 'x' = side length of equilateral Δ

$\sqrt{3}$ / 1 = 21 / x

cross-multiply:

$\sqrt{3}$x = 21

x = 21 / $\sqrt{3}$

rationalize the denominator by multiplying numerator and denominator by $\sqrt{3}$

21$\sqrt{3}$ / $\sqrt{3}$·$\sqrt{3}$ = 21$\sqrt{3}$ / 3 or 7$\sqrt{3}$