| The perimeter of a rhombus is 100 cm. If one of its diagonals is 14 cm, then the area of the rhombus is |
A) \[144\,\,c{{m}^{2}}\]
B) \[225\,\,c{{m}^{2}}\]
C) \[336\,\,c{{m}^{2}}\]
D) \[400\,\,c{{m}^{2}}\]
Correct Answer: C
Solution :
| Side of rhombus \[=\frac{1}{2}\sqrt{d_{1}^{2}+d_{2}^{2}}\] |
| Perimeter of rhombus \[=4\times \frac{1}{2}\sqrt{d_{1}^{2}+d_{2}^{2}}\] |
| \[\therefore \] \[2\sqrt{d_{1}^{2}+d_{2}^{2}}=100\] |
| \[\Rightarrow \] \[d_{1}^{2}+d_{2}^{2}=2500\] |
| \[\Rightarrow \] \[{{(14)}^{2}}+d_{2}^{2}=2500\] |
| \[\Rightarrow \] \[d_{2}^{2}=2340\]\[\Rightarrow \]\[{{d}_{2}}=48\] |
| \[\therefore \]Area of rhombus \[=\frac{1}{2}\times {{d}_{1}}\times {{d}_{2}}\] |
| \[=\frac{1}{2}\times 14\times 48=336\,\,c{{m}^{2}}\] |
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