Question

How many times area is changed, when sides of a triangle are doubled.

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Answer 1

Step-by-step explanation:

Let the sides of the given triangle be a, b and c.

Semi-perimeter = a+b+c /2

Area of triangle = √s (s-a) (s-b) (s-c)

Given that the sides of the triangle are doubled.

That is sides of new triangle are 2a, 2b and 2c.

Semi-perimeter= a+b+c = 2s

Area of triangle = √2s (2s-2a)(2s-2b) (2s-2c)

=√16s (s-a)(s-b)(s-c)

= 4 √s(s-a)(s-b)(s-c)

So The are of the new triangle is 4 times that of the old triangle

But the increase in area = 4Δ-1Δ =3Δ

The increase in area is 4 times

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