In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio...

JAMB 1987

In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio of the area of triangle PQR to the area of the trapezium QRST.

A. 4:9
B. 4:5
C. 1:3
D. 2:3

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Correct Answer: Option B

Explanation

h₁ = \(\frac{h_1 + h_2}{1.5}\) = \(\frac{h_1}{h_2} = 2\)

\(\frac{A_{\bigtriangleup PQR}}{A_{TP(QRST)}} = \frac{\frac{1}{2} \times 2 \times h_1}{\frac{1}{2} \times h_2 (2 + 3)}\)

\(\frac{2}{5} \times \frac{h_1}{h_2} = \frac{2}{5} \times 2\)

= \(\frac{4}{5}\)

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