A side of a rectangle is three times the other. If the perimeter increases by...

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 = \(0.0404 \times 100 = 4.04%\)