WAEC 2021 · Paper 2 · Q4

The sides of a rectangle are $(x + 3)\text{ cm}$ and $(x - 2)\text{ cm}$ . If the area of the rectangle is $36\text{ cm}^2$ , find its:

(a)
dimensions;
Separate values with commas, e.g. 3, −2
(b)
perimeter.

Worked solution (try it first)

(a)

Area $= (x + 3)(x - 2) = 36$ .
Expand: $x^2 + x - 6 = 36$ , so $x^2 + x - 42 = 0$ and $(x + 7)(x - 6) = 0$ .
$x = -7$ would make the sides $-4$ and $-9$ , which is impossible, so $x = 6$ .
The rectangle is 9 cm by 4 cm.

(b)

Perimeter $= 2(9 + 4) = 26$ cm.

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