question_answer

The altitude drawn to the base oisosceles  triangle is 8 cm and the perimeter is 32 cm. The area of the triangle is            

A) \[60.25\,c{{m}^{2}}\]             

B) \[70\,c{{m}^{2}}\]      

C) \[80\,c{{m}^{2}}\]                  

D)        \[48\,c{{m}^{2}}\]

Correct Answer: D

Solution :

[d]AB=AC=x, BC=32-2x \[\therefore \] BD = 16 - x, Also AD = 8 (given) \[A{{B}^{2}}=B{{D}^{2}}+A{{D}^{2}}\] \[\Rightarrow {{x}^{2}}={{8}^{2}}+{{(16-x)}^{2}}\]which gives x =10.                    \[\therefore \text{ }BC=32-20=12\,\,cm.\] Area of the triangle              \[=\frac{1}{2}~~BC\times AD~\] \[=\frac{1}{2}\times 12\times 88\,\,\,c{{m}^{2}}=48\,\,c{{m}^{2}}\]