question_answer

A 12 cm rod is held between a flashlight and a wall as shown. Find the length of the shadow on the wall if the rod is 45 cm from the wall and 15 cm from the light.        

A)  75 cm

B)         96 cm

C)  48 cm

D)         60 cm

Correct Answer: C

Solution :

In \[\Delta AED\]and \[\Delta ABC\] we have In \[\Delta ADM\] and \[\Delta ABF\] \[\angle DAM=\angle BAF\]    (Common) \[\angle DMA=\angle BFM\] (Corresponding angles) \[\therefore \]  \[\Delta ADM\tilde{\ }\Delta ABF\]          (By AA similarity) \[\Rightarrow \] \[\frac{AD}{AB}=\frac{DM}{BF}=\frac{AM}{AF}\] or \[\frac{DM}{BF}=\frac{AM}{AF}\] \[\Rightarrow \]  \[\frac{6}{BF}=\frac{15}{60}\]\[\Rightarrow \] \[BF=25\,cm\] \[\therefore \] \[BC=BF+FC=2BF=48\,cm\]                                     \[(\because \,\,CF=BF)\]