Given that the area of an equilateral triangle is 278 cm2, find its perimeter.

Answer 1

Do you know that a 30°-60°-90° triangle is half of an equilateral triangle?

The formula for the area of a triangle involving 2 sides and one angle is"

Area = (1/2)ab sin C

a = hypotenuse of the 30°-60°-90° triangle = one side of the equilateral triangle

b = half of the hypotenuse of the 30°-60°-90° triangle = (1/2)a

C= 60°

Area = area of the 30°-60°-90° triangle = (1/2)278

(1/2)278 = (1/2)a(1/2)a sin 60°

139 = (1/4)a²(√3 /2)

139 = (√3 /8)a²

Multiply 8/√3 on both sides:

1112/√3 = a²

a=25.34

Perimeter is P=3a = 3(25.34)

P= 76.01cm