Question

if the perimeter of an equilateral triangle is a number half size of its area, how long is each side?

Answer 1

The area is A=(√3/4)a^2
The perimeter is p=3a

3a = 1/2(√3/4)a^2 -->equation (perimeter is 1/2 size of the area)

3a = (√3/8)a^2

3/a = √3/8

a = 3/(√3/8) = 24/√3 * √3/√3 = 24√3/3 = 8√3 -->rationalized the denominator by multiplying the equivalent of 1.

If you check this answer with the equation, it should work.