question_answer

In \[\Delta \mathbf{PQR}\], the line drawn from the vertex P intersects QR at a point S. If QR = 4.5 cm and SR = 1.5 cm then the ratios of the area of triangle PQS and triangle PSR is

A)  4 : 1                            

B)  3 : 1            

C)  3 : 2                            

D)  2 : 1

Correct Answer: D

Solution :

(d): \[QR=4.5\]cm \[SR=1.5\]cm \[\therefore QS=4.5-1.5=3\]cm \[\frac{\Delta PQS}{\Delta PSR}=\frac{\frac{1}{2}\times h\times QS}{\frac{1}{2}\times h\times SR}\] \[=\frac{3}{1.5}=2:1\]