question_answer

Base of a right angled \[\Delta \,ABC\] is 16 times the base of another right angled triangle PQR and height of first right angled triangle is 1/6th of other?s height, then what will be ratio of area of first triangle to second triangle.

A)  \[16:3\]                        

B)  \[8:3\]   

C)  \[1:1\]                          

D)  \[4:3\]

Correct Answer: B

Solution :

(b):                                                                 \[\frac{BC}{QR}=\frac{16}{1}\] and \[\frac{AB}{PQ}=\frac{1}{6}\] Area \[\Delta \,(1)=\frac{1}{2}.x.16y=8xy\] Area \[\Delta \,(2)=\frac{1}{2}6x.y=3xy\] \[\therefore \] Ratio = \[8:3\]