question_answer

If the perimeter of a rhombus is 80 cm and one of its diagonal is 24 cm, then what is the area \[(in\,\,c{{m}^{2}})\] of the rhombus?

A)  218                 

B)  192

C)  384                             

D)  768

Correct Answer: C

Solution :

[c] \[\because \] Perimeter of rhombus = 80 cm \[\therefore \] Side of rhombus \[=\frac{80}{4}=20\,\,cm\] By Pythagorean theorem, \[{{(20)}^{2}}={{(12)}^{2}}+({{x}^{2}})\] \[\therefore \,\,\,{{x}^{2}}=400-\,144=256\] \[\therefore x=\sqrt{256}=16\,\,cm\] \[\therefore \] Diagonal of rhombus \[=2x=2\times 16=32\,\,cm\]and other diagonal=24 cm \[\therefore \]  Area of rhombus \[=\frac{1}{2}\times {{d}_{1}}\times {{d}_{2}}\] \[=\frac{1}{2}\times 24\times 32=384\,\,c{{m}^{2}}\]