question_answer

If a tree casts a 18 feet shadow and at the same time, a child of height 3 feet casts a 2 feet shadow, then the height the tree is        

A)  27 feet            

B)         32 feet

C)                     45 feet            

D)         36 feet

Correct Answer: A

Solution :

Let AB be the height of tree which casts a shadow \[AC=18\]feet and ED be the height of child which casts a shadow \[CD=2\]feet. Now, in \[\Delta ABC\]and \[\Delta DEC\], we have                         \[\angle A=\angle D\]                   [Each \[{{90}^{o}}\]] \[\angle C=\angle C\]              [Common angle] \[\therefore \]  \[\Delta ABC\tilde{\ }\Delta DEC\]       [By AA similarity] \[\Rightarrow \]            \[\frac{AB}{DE}=\frac{AC}{DC}\] \[\Rightarrow \]            \[\frac{AB}{3}=\frac{18}{2}\] \[\Rightarrow \]            \[AB=27\] feet So, the height of tree is 27 feet.