In triangle PQR, ∠PQR = 30° and ∠PRQ = 45°. If S is a point on QR such that QS : QR = 2 : 5, then find the ratio of the area of triangle PQS to that of triangle SPR.

A.
B.
C. 3 : 2
D. 2 : 3

Question

In triangle PQR, ∠PQR = 30° and ∠PRQ = 45°. If S is a point on QR such that QS : QR = 2 : 5, then find the ratio of the area of triangle PQS to that of triangle SPR.

A. 
	B. 
	C. 3 : 2
	D. 2 : 3

shubhamsrg · Answer

|dw:1340186877047:dw|
let M be a point on QR such that PM is perpendicular to QR.
area of PQS = 1/2 PM.QS
and area of PSR = 1/2 PM.SR
thus area(PQS)/area(PSR)  = QS/SR
or area(PSR)/area(PQS) = SR/QS = (QR - QS)/QS = QR/QS - 1 = 5/2 -1 = 3/2
hence req ans should be 2:3