A) \[(5\sqrt{3}+\sqrt{11})cm\]
B) \[(5\sqrt{3}+\sqrt{7})cm\]
C) \[(3\sqrt{5}+11)cm\]
D) \[\left( \frac{5\sqrt{3}+11}{3} \right)cm\]
Correct Answer: A
Solution :
Draw\[BP\bot AC\] Now in right angled\[\Delta APB\] \[\frac{AP}{AB}=\cot {{30}^{o}}\] \[AP=\frac{10\sqrt{3}}{2}=5\sqrt{3}cm\] Also, \[\frac{BP}{AB}=\sin {{30}^{o}}\] \[\Rightarrow \] \[BP=AB\sin {{30}^{o}}\] \[=10\times \frac{1}{2}=5\,\,cm\] Also in\[\Delta BPC\] \[B{{P}^{2}}+P{{C}^{2}}=B{{C}^{2}}\] \[\Rightarrow \] \[{{5}^{2}}+P{{C}^{2}}={{6}^{2}}\] \[\Rightarrow \] \[P{{C}^{2}}=36-25=11\] \[\Rightarrow \] \[PC=\sqrt{11}cm\] \[\therefore \] Longer diagonal, \[=\left( 5\sqrt{3}+\sqrt{11} \right)cm\]You need to login to perform this action.
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