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Question

If each side of a triangle is tripled then find its percentage increased in area?

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Solution

Let the initial side be a units

Area = (√3)a²/4 sq. units

Now, side is tripled,
new side, a' = 3a

New area = (√3)(3a)²/4
=9×[(√3)a²/4]
=9×(initial area)

Increase in area = 9×(initial area) - (initial area) = 8 ×(initial area)

% increase = (increase/initial area)×100
=[8 ×(initial area)/(initial area)]×100
= 800 %

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