| The perimeter of the triangular base of a right prism is 60 cm and the sides of the base are in the ratio 5: 12: 13. Then, its volume will be (height of the prism being 50 cm) |
A) \[6000\,\,c{{m}^{3}}\]
B) \[6600\,\,c{{m}^{3}}\]
C) \[5400\,\,c{{m}^{3}}\]
D) \[9600\,\,c{{m}^{3}}\]
Correct Answer: A
Solution :
| Let the sides of the base are \[5x,\]\[12x\]and \[13x\]respectively. |
| Given, perimeter of base = 60 cm |
| \[\Rightarrow \] \[5x+12x+13x=60\] |
| \[\therefore \] \[x=\frac{60}{30}=2\] |
| The sides of base are \[10\,\,cm,\]\[24\,\,cm\]and \[26\,\,cm.\] |
| \[\therefore \]Volume of prism |
| \[=\frac{1}{2}\times 10\times 24\times 50=6000\,\,c{{m}^{3}}\] |
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