question_answer

If A and B are two points on the line \[3x+4y+15=0\]such that \[OA=OB=9\]units, then the area of the triangle \[OAB\] is 

A)            18 sq. units                               

B)            \[18\sqrt{2}sq.\]units

C)            18/\[\sqrt{2}\]sq. units            

D)            None of these

Correct Answer: B

Solution :

           \[OA=OB=9,OD=\frac{15}{\sqrt{25}}=3\]                    Therefore\[AB=2AD=2\sqrt{81-9}=2\sqrt{72}=12\sqrt{2}\]                    Hence \[\Delta =\frac{1}{2}(3\times 12\sqrt{2})=18\sqrt{2}\] sq. units.