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
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})