question_answer

The base of an isosceles triangle is 20cm and its area is \[200\,\,c{{m}^{2}},\]find its perimeter.

A) \[20\left( \sqrt{3}+1 \right)cm\]          

B) \[20\left( \sqrt{5}+1 \right)cm\]

C) \[20\sqrt{5}cm\]                     

D) \[20\sqrt{3\,\,cm}\]

Correct Answer: C

Solution :

Let \[\Delta ABC\] be an isosceles triangle and                            Let\[AL\bot BC.\]                                 \[\frac{1}{2}\times BC\times AL=200\,\,c{{m}^{2}}\] \[\frac{1}{2}\times 20\,\,cm\times AL=200\,\,c{{m}^{2}}\] \[AL=\frac{200\times 2}{20}=20\,\,cm\] Now, \[BL=\frac{1}{2}BC=\left( \frac{1}{2}\times 20 \right)cm=10\,\,cm\] and \[AL=20\,\,cm\] \[\therefore \]\[a=\sqrt{A{{L}^{2}}+B{{L}^{2}}}=\sqrt{{{20}^{2}}+{{10}^{2}}}cm\] \[=\sqrt{400+100}=\sqrt{500}=10\sqrt{5}cm\] Hence perimeter \[=\left( 10\sqrt{5}+10\sqrt{5}+20 \right)\]\[=20\sqrt{5}+20=20\left( \sqrt{5}+1 \right)cm\]