Question

The percentage increase in the area of a triangle if its each side is doubled will be

Answer 1

Answer:300 %

Step-by-step explanation:

Let the sides of the given triangle be x, y and z.

Semi-perimeter S' = x+y+z/2

Area of triangle A' = √S'(S'-x) (S'-y) (S'-z)

Given that the sides of the triangle are doubled.

That is sides of new triangle are 2x, 2y and 2z

Semi-perimeter S = 2x+2y+2z/2= 2S'

Area of new triangle

= √2S'(2S'-2x) (2S'-2y) (2S'-2z)

= √2S'×2(S'-x) 2(S'-y) 2 (S'-z)

= √16S'(S'-x) (S'-y) (S'-z)

=4√S'(S'-x) (S'-y) (S'-z)

= 4A'

Increase = 4A'-A'= 3A'

% increase

=3A'/A' X 100

= 300 %