If there is threefold increase in all the sides of a cyclic quadrilateral, then the percentage increase in its area will be: ?->(Show Answer!)

1. If there is threefold increase in all the sides of a cyclic quadrilateral, then the percentage increase in its area will be:

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By: anil on 05 May 2019 02.40 am

Let $$a, b, c$$ and $$d$$ be the sides of the cyclic quadrilateral.
Thus, $$s = frac{(a+b+c+d)}{2}$$
$$Area = sqrt{(s-a)(s-b)(s-c)(s-d)}$$
Thus, after a threefold increase in the sides the sides will become $$4a, 4b, 4c$$ and $$4d$$.
Thus new $$s = s_{new} = (4a+4b+4c+4d)/2 = 4s$$
Thus, $$Area_{new} = sqrt{(4s-4a)(4s-4b)(4s-4c)(4s-4d)}$$
= $$sqrt{4*4*4*4*(s-a)(s-b)(s-c)(s-d)}$$ = $$16*Area$$
Thus, there is 1500% increase in the area.
Hence, option D is the correct answer.

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