Question

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

option is given below:
1) 306.25%
2) 103.125%
3) 206.25%
4) 105.125%

Answer 1

Let h,a and a be the sides of right angled isosceles triangle.
then area (A1)= (1/2)*a*a 
Now, all the sides are increased by 75%
Therefore, the new sides are 1.75h, 1.75a and 1.75a respectively.
The new area(A2) = (1/2)*(1.75a)(1.75a) = [(1/2)*a*a]$( 1.75^{2} )$
                       = 3.0625*(A1)
Therefore new area A2 is 3.0625 times of original area A1

% change = [(A2 - A1)/A1]*100 = 206.25%

Please note that % change is 206.25%  (A1 + 2.0625A1) and  % increase is 3.0625 times (A2 = 3.0625*A1)

Answer is 206.25%