Question

The area of an equilateral triangle is numerically equal to its perimeter find its perimeter correct to 2 decimal places

Answer 1

Area of a triangle = 1/2 x base x height 

Let the equilateral triangle have side = x 

Area = 1/2 X x X h 

h^2 = x^2 - (1/2x)^2 = x^2 - 1/4x^2 

= 3/4 x^2 

h = \/3 .x/2 

Area = 1/2 X x X \/3 .x/2 = \/3x^2/4 

Perimeter = 3x 

3x = \/3 x^2 /4 
3 = \/3 x/4 
12/\/3 = x 

x = 6.93 ANSWER