If each side of a triangle is tripled find change in% in its area.explain it with full steps

Solution:- Let, the initial sides of triangle be 'a', 'b', and 'c'. Then, semi-perimeter of triangle will be-

s = (a+b+c)/2 and Area of triangle (A) = √s(s-a)(s-b)(s-c).

Now, if each side is tripled. Then, new sides will be 3a, 3b, and 3c. And, semi-perimeter of triangle will be- s'' = (3a+3b+3c)/2  = 3s

and, New area of triangle (A'') = √s''(s''-3a)(s''-3b)(s''-3c) = √3s(3s-3a)(3s-3b)(3s-3c)

                                    A'' = 9 √s(s-a)(s-b)(s-c) = 9A

% change in Area = [(A'' - A)/A] x 100 %

                         = [(9A- A)/A] x 100 % = 800% [ANS]

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.

All the best!!!

Regards,
Askiitians Experts
Priyansh Bajaj