A side of a rectangle is three times the other. If the perimeter increases by 2%, find the percentage increase in the area of the rectangle.
Explanation
Area, (A = 3x^{2})
Perimeter, (P = 8x)
(therefore A = frac{3P^{2}}{64})
Let (P_{1}) and (A_{1}) be the new perimeter and area respectively.
Perimeter increases by 2%
(therefore P_{1} = 1.02P)
(A_{1} = frac{3(1.02P)^{2}}{64})
(frac{A_{1}}{A} = frac{3(1.02P)^{2}}{64} times frac{64}{3P^{2}})
= 1.0404
(A_{1} = 1.0404A = A + 0.0404A)
Increase in A = 0.0404A.
% increase = (0.0404 times 100 = 4.04%)