JAMB 1987 · UME · Q32

In the diagram, $QR \parallel TS$ and $QR : TS = 2 : 3$ . Find the ratio of the area of triangle $PQR$ to the area of the trapezium $QRST$ .

Worked solution (try it first)

$QR \parallel TS$ , so triangles $PQR$ and $PTS$ are similar with lengths in the ratio $2 : 3$ .
Areas of similar figures are in the ratio of the squares of the lengths: $2^2 : 3^2 = 4 : 9$ .
The trapezium is the big triangle minus the small one: $9 - 4 = 5$ parts.
So the ratio is $4 : 5$ , option B.