WAEC 2008 · Paper 2 · Q5

(a)
A rectangular field is $l$ metres long and $b$ metres wide. Its perimeter is $280$ metres. If the length is two and a half times its breadth, find the values of $l$ and $b$ .
Separate values with commas, e.g. 3, −2
(b)
The base of a pyramid is a $4.5\text{ m}$ by $2.5\text{ m}$ rectangle. The height of the pyramid is $4\text{ m}$ . Calculate its volume.

Worked solution (try it first)

(a)

The perimeter of a rectangle is $2(l + b)$ , so $2(l + b) = 280$ and $l + b = 140$ .
The length is two and a half times the breadth: $l = 2.5b$ .
Substitute: $2.5b + b = 140$ , so $3.5b = 140$ and $b = 40$ .
Then $l = 2.5 \times 40 = 100$ .
The field is $100\text{ m}$ long and $40\text{ m}$ wide.

(b)

The volume of a pyramid is $\frac13 \times \text{base area} \times \text{height}$ .
The base area is $4.5 \times 2.5 = 11.25\text{ m}^2$ .
$V = \frac13 \times 11.25 \times 4 = 15$ .
The volume is $15\text{ m}^3$ .

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