Question

In a right angled isosceles triangle, if it's sides are increased by 75%,then the percentage change in its area is

Answer 1

let the sides of the right angled isosceles triangle is a,a,b where hypotaneous=b and base=height=a
now its area is 1/2*base*height =1/2*a*a=(1/2)*a^2
again when it increases its sides by 75% then its base =height =a+75a/100=7a/4
so then its area will be 1/2*7a/4*7a/4=49a^2/32
change in area
=( 49/32)a^2-(1/2)a^2=(33/32)a^2
so change in area percentage
=[((33/32)a^2)/((1/2)a^2)]*100
=206.25%