question_answer

\[\Delta \]ABC Is a right angled triangle whose \[\angle \]C = \[90{}^\circ \], if \[\overline{CD}\bot \overline{AB}\]and \[{{\overline{BC}}^{2}}=\text{ }16,\text{ }{{\overline{CA}}^{2}}=9\]find  \[\overline{CD.}\]

A)  \[\frac{5}{12}\]                        

B)  \[\frac{12}{5}\]

C)  5                                

D)  12

Correct Answer: B

Solution :

                                  \[A{{B}^{2}}=A{{C}^{2}}+B{{C}^{2}}=9+16=25\] \[\therefore \] \[AB=\sqrt{25}=5\] Area of \[\Delta \,ABC~=\frac{1}{2}\times AB\times CD\] \[\Rightarrow \]\[\frac{1}{2}\times 4\times 3=\frac{1}{2}\times 5\times CD\] \[\Rightarrow \] \[CD=\frac{12}{5}\]