WAEC 2021 · Paper 2 · Q8

(a)
In $\triangle PQR$ , $\angle PQR = 90^\circ$ . If its area is $216\text{ cm}^2$ and $|PQ| : |QR|$ is $3 : 4$ , find $|PR|$ .
(b)
The present ages of a man and his son are 47 years and 17 years respectively. In how many years would the man's age be twice that of his son?

Worked solution (try it first)

$|PQ| : |QR| = 3 : 4$ , so let $|PQ| = 3k$ and $|QR| = 4k$ .
The right angle is at $Q$ , so these two sides are the base and height: area $= \frac12 \times 3k \times 4k$
$= 6k^2$
$= 216$ .
So $k^2 = 36$ and $k = 6$ .
The sides are 18 cm and 24 cm.
By Pythagoras, $|PR| = \sqrt{18^2 + 24^2}$
$= \sqrt{900}$
$= 30\text{ cm}$ .