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

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.

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

View answer & explanation

Correct answer is B

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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