Find the percentage increase in the area of a triangle if each side is increased by N times.

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Solution

In similar triangles, ratio of areas is equal to ratio of the square of corresponding sides.
Area 2/Area 1 = (side 2/side 1)²

Side2/side1=N^2

So Area2=N^2×Area1

Change in area=(N^2-1)×Area1

Therefore percentage change in area=(N^2-1)×Area1×100/Area1

=(N^2-1)×100

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