Question

The area of an equilatoral triangle ABC is 50cm^2 . Find AB.

Answer 1

We know all angles are 60° and all sides are equal.
Let the side be x cm

(1/2)(x)(x)sin60° = 50
x^2 = 100/(√3/2) = 200/√3
x = 10√2/(√√3)) = appr. 10.75 cm

or let each side be 2x
then the height is √3 x

area = (1/2)(2x)(√3x) = 50
√3x^2 = 50
x^2 = 50/√3
x = 5.3728 appr.
so 2x, the side is appr. 10.75

Answer 2

Area = (1/2)*base*(base/2)*sqrt3
= (sqrt3)(base)^2/4 = 50

base^2 = 200/sqrt3 = 115.47
base = 10.7456599

All sides have that length, since the triangle is equilateral.