Question

find the percentage decrease in the area of triangle if each of its side is halved

Answer 1

There would be a 75% decrease. The shortest method is to observe that the question implies one particular value for the % change. So, we can assume any convenient triangle for this purpose and end up with the right answer, as the choice of triangle shouldn’t affect the value.

Area of equilateral triangles can be found out straight-away using the formula

Δi=3–√a24

On halving the sides, we get

Δf=3–√a216=Δi4

So, percentage change =Δf−ΔiΔi×100

=14−11×100

=75% decrease