WAEC 2018 · Paper 2 · Q3

(a)
The diagonals of a rhombus are $10.2\text{ cm}$ and $9.3\text{ cm}$ long. Calculate, correct to one decimal place, the perimeter of the rhombus.
(b)
Given that $\sin x = \frac35$ , $0^\circ < x < 90^\circ$ , find the value of $5\cos x - 4\tan x$ .

Worked solution (try it first)

(a)

The diagonals of a rhombus cut each other in half at right angles.
So each side is the hypotenuse of a right-angled triangle with legs $\frac{10.2}{2} = 5.1$ cm and $\frac{9.3}{2} = 4.65$ cm.
Side $= \sqrt{5.1^2 + 4.65^2}$
$= \sqrt{26.01 + 21.6225}$
$= \sqrt{47.6325}$
$\approx 6.902$ cm.
The four sides are equal, so the perimeter is $4 \times 6.902 \approx 27.6$ cm.

(b)

$\sin x = \frac35$ gives a right-angled triangle with sides 3, 4 and 5, so $\cos x = \frac45$ and $\tan x = \frac34$ .
Then $5\cos x - 4\tan x = 5 \times \frac45 - 4 \times \frac34$
$= 4 - 3$
$= 1$ .

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