If every side of a triangle is doubled, then increase in the area of the triangle is
(a) `100sqrt(2) %`
(b) 200%
(c) 300%
(d) 400%

Explanation

If the side of a triangle is doubled than their length of sides will be 2a,2b,2c
Nowas we know that the semi-perimeter of the triangle is :
`s=(a+b+c)/2`______1
`s^'=(2a+2b+2c)/2`_____2
`s^'=2s`
`therefore` area of`triangle = sqrt( s(s-a)(s-b)(s-c))`
So, area of new `triangle^'`= `sqrt(2s(2s-2a)(2s-2b)(2s-2c)`
`4sqrt(s(s-a)(s-b)(s-c))`
4`triangle`
`therefore` Increase in area =4`triangle`-`triangle`
3`triangle`
% Increase =`(3 trianglexx100)`/(`triangle`)
300%