question_answer

The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of these sides is 13 cm. Its area is

A)  \[72\,c{{m}^{2}}\]                         

B)  \[12\sqrt{35}\,c{{m}^{2}}\]

C)  \[24\sqrt{35}\,c{{m}^{2}}\]          

D)  \[150\,c{{m}^{2}}\]

Correct Answer: B

Solution :

    As shown in the diagram, area of triangle ABC \[=1/2\]area of the parallelogram ABCD. By Heron's formula, area of triangle \[=\sqrt{S\left( S-a \right)\left( S-b \right)\left( S-c \right)}\] Here \[S=\frac{9+8+13}{2}=15\] \[\therefore \] Area of ABC\[=\sqrt{15(6)(2)(7)}\] \[\sqrt{6\times 7\times 30}=6\sqrt{35}\,\text{sq}\text{.}\,cm.\] Hence, area of ABCD \[=2\times 6\sqrt{35}=12\sqrt{35}\,\text{sq}\text{.m}\]