question_answer

In \[\Delta PQR\], 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 :

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