119k views
14 votes
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

User YMM
by
6.7k points

1 Answer

7 votes

Answer:

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)

User Jdpjamesp
by
7.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.