WAEC 2013 · Paper 2 · Q3

(a)
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.

Worked solution (try it first)

Let the sides be $x$ and $3x$ .
The perimeter is $P = 8x$ and the area is $A = 3x^2$ .
$P$ is a fixed multiple of $x$ , so a 2% increase in $P$ means a 2% increase in $x$ .
For a small change, $\dfrac{\delta A}{A} \approx \dfrac{6x\,\delta x}{3x^2}$
$= 2\dfrac{\delta x}{x}$ .
So the area increases by about $2 \times 2\% = 4\%$ .
(Exactly, $1.02^2 - 1 = 4.04\%$ .)