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.
Attached Figure / Diagram
A
4:9
B
4:5
C
1:3
D
2:3
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
h1 = \(\frac{h_1 + h_2}{1.5}\) = \(\frac{h_1}{h_2} = 2\)
\(\frac{A_{\bigtriangleup PQR}}{A_{TP(QRST)}} = \frac{\frac{1}{2} \times 2 \times h_1}{\frac{1}{2} \times h_2 (2 + 3)}\)
\(\frac{2}{5} \times \frac{h_1}{h_2} = \frac{2}{5} \times 2\)
= \(\frac{4}{5}\)
Source: Myschool Past Questions Archive (Record #32824)