question_answer

A tin sheet is in the form of a rhombus whose side is 5 cm and one of its diagonals is 8 cm. Then the cost of painting the sheet at the rate of Rs. 3.50 per\[c{{m}^{2}}\]on both of its sides is

A) Rs. 84                         

B) Rs. 140

C) Rs. 168          

D) none of these

Correct Answer: C

Solution :

    Diagonals of a rhombus bisect each other at \[90{}^\circ .\] In \[\Delta OAB,\]\[OB=\sqrt{{{5}^{2}}-{{4}^{2}}}=3\,cm\] \[\therefore \]    \[BD=2\times OB=2\times 3=6\,cm\] \[\therefore \]    Area of ABCD\[=\frac{1}{2}\times 8\times 6=24\,c{{m}^{2}}\] Now, the cost of painting \[=2\times 3.50\times \]area of rhombus ABCD \[=2\times 3.50\times 24\] \[=\text{Rs}\text{.}\,168\]