Question

If every side of a triangle is doubled, then increase in the area of the triangle is

(a) $100\sqrt{2}\%$

(b) 200%

(c) 300%

(d) 400%

Answer 1

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

, where

We take the sides of a new triangle as 2a, 2b, 2c that is twice the sides of previous one

Now, the area of a triangle having sides 2a, 2b, and 2c and as semi-perimeter is given by,

Where,

Now,

Therefore, increase in the area of the triangle

Percentage increase in area

Therefore, the answer is (c).