Indian Institute of Foreign Trade 2009 Solved Paper

Question : 122 of 122

Marks: +1, -0

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

Solution:

Let a,b,c and be the sides of the cyclic quadrilateral
Thus,

s={(a+b+c+d)}/2

Area

=√{(s-a)(s-b)(s-c)(s-d)}

Thus, after a threefold increase in the sides the sides will become and .
Thus new

s=s_{\text "new"}={(4a+4b+4c+4d)/2=4s}

Thus,

\Area_{\text"new"}=√{(4s-4a)(4s-4b)(4s-4c)(4s-4d)}

=√{4×4×4×(s-a)(s-b)(s-c)(s-d)}=16*\;\text"Area"\;

Thus, there is 1500% increase in the area.
Hence, option D is the correct answer.

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