Question

If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the area?

Answer 1

let the original length be a

length is being increased by 50%

:.the new side will be a+a/2=3a/2

ar(equilateral triangle)=√3/4×(side)²
=√3/4×9a²/4
=9√3 a²/16

% increase=ar(equilateral increased triangle)-ar(equilateral triangle)/ar(equilateral triangle)×100%

= (9√3 a²/16-√3 a²/4)/√3 a²/4×100
=√3 a²/4(9/4-1)/√3 a²/4×100%
=5/4×100%
=1.25×100
=125%