Question

if each side of a triangle is doubled then how many times the area of the triangle increased​

Answer 1

Given,

In an Isosceles Triangle,

First Side = a
Second Side = b
Third side = c

=> S = a+b+c/2

$Ar_{Old} = \sqrt{S(S-a)(S-b)(S-c)}$

New Side = 2a, 2b and 2c.

=> S' = 2a+2b+2c/2

=> S' = 2(a+b+c/2)

=> S' = 2S [ a+b+c/2 = S]

$Ar_{New} = \sqrt{S'(S'-2a)(S'-2b)(S'-2c)}$

$Ar_{New} = \sqrt{2S(2S-2a)(2S-2b)(2S-2c)}$

$Ar_{New} = \sqrt{2\times2\times2\times2\times S(S-a)(S-b)(S-c)}$

$Ar_{New} = 4 \sqrt{S(S-a)(S-b)(S-c)}$

$\bold{Ar_{New} = 4\times Ar_{Old}}$

Hence, Area of New triangles will be 4 times the area of old triangle.