WAEC 2009 · Paper 2 · Q8

The area of a rectangular football field is $7200\text{ m}^2$ and its perimeter is 360 m.

(a)
Calculate the dimensions of the field.
Separate values with commas, e.g. 3, −2
(b)
Calculate the cost of clearing the field at ₦6.50 per square metre, leaving a margin 2 m wide along the longer sides.
(c)
Calculate the percentage of the field not cleared.

Worked solution (try it first)

(a)

Let the length be $x$ m and the breadth $y$ m: $xy = 7200$ and $2(x + y) = 360$ , so $x + y = 180$ .
Substitute $y = 180 - x$ : $x(180 - x) = 7200$ , so $x^2 - 180x + 7200 = 0$ .
Factorise: $(x - 120)(x - 60) = 0$ .
The field is 120 m long and 60 m wide.

(b)

A 2 m margin along each longer side takes 4 m off the breadth: the cleared part is $120 \times 56 = 6720\text{ m}^2$ .
Cost $= 6720 \times 6.50 = 43\,680$ , so ₦43,680.00.

(c)

Area not cleared $= 7200 - 6720 = 480\text{ m}^2$ .
Percentage $= \frac{480}{7200} \times 100$
$= 6\frac23\%$
$\approx 6.67\%$ .

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