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

  1. 250
  2. 300
  3. 400
  4. 200
Manish Listener Asked on 28th October 2014 in Maths.
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1 Answer(s)

Answer: (2) 300
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

Anurag Mishra Professor Answered on 14th July 2015.
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