Lines QR and ST are parallel; the shortest distance between them is half the shortest distance between point P and line QR. Find the ratio of area(ΔPST) to area(trapezium SQRT).
Options:
(A) 1/3
(B) 1/4
(C) 2/5
(D) 1/2
Official Answer Key:
A
Step-by-Step Solution & Explanation
Let h = distance from P to QR. ST lies at height h/2 from QR ⇒ P to ST height = h − h/2 = h/2. ΔPST ~ ΔPQR with linear ratio (h/2)/h = 1/2, so Area(ΔPST) = (1/2)² × Area(ΔPQR) = ¼ Area(ΔPQR). Area(trapezium SQRT) = Area(ΔPQR) − Area(ΔPST) = ¾ Area(ΔPQR). Ratio = (¼)/(¾) = 1/3.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.