# Percentage increase in the area of triangle if side is doubled.

Each side of a triangle is doubled. The percentage increase in the area of the triangle is

- 250
- 300
- 400
- 200

**Answer: (2) 300**

**Explanation:-
**Let p, q, r be the sides of the triangle

Then, the perimeter of the triangle (S) = ( p + q + r)/2.

According to the question,

The sides of new triangle are 2p, 2q and 2r.

Then, the perimeter of new triangle = 2(p + q + r)/2 = 2S

The area of the first triangle = [S (S – p) (S – q) (S – r)]

^{1/2}

The area of new triangle = [2S (2S – 2p) (2S -2q) (2S – 2r)]

Thus, the area of new triangle = 4 x Area of first triangle

Increase in the area of the triangle = 4 x Area of the first triangle – Area of the first triangle

= 3 x the area of the first triangle

Increase area in percent = 3 x area of first triangle x 100/Area of first triangle

= 300%

Hence, the answer is (2) 300