Question

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

Answer 1

Let the sides of the given triangle be a, b and c.
Semi-perimeter,
Area of triangle
Given that the sides of the triangle are doubled.
That is sides of new triangle are 2a, 2b and 2c.
Semi-perimeter
s= 2a+2b+2c/2= 2(a+b+c/2) = 2s.

area of the triangle = root over 2s* (2s-2a) (2s-2b) (2s-2c) = root over 16s(s-a) (s-b)(s-c) = 4 root over s(s-a)(s-a)(s-c) therefore 4*triangle increased area = 4(area) - area of the previous triangle. = 3times