| 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) (a)\[6000\text{ }c{{m}^{3}}\]
B) \[6600\text{ }c{{m}^{3}}\]
C) (c)\[5400\text{ }c{{m}^{3}}\]
D) \[9600\text{ }c{{m}^{3}}\]
Correct Answer: A
Solution :
| Let sides be 5x, 12x and 13x, respectively. |
| Then, \[5x+12x+13x=60\] |
| \[30x=60\]\[\Rightarrow \]\[x=2\] |
| \[\therefore \] Sides are 10, 24 and 26. |
| Now, \[{{26}^{2}}={{24}^{2}}+{{10}^{2}}\] |
| Here, base of triangle is right angled triangle. |
| \[\therefore \] Area of base \[=\frac{1}{2}\times 10\times 24=120\] |
| Volume of the prism = Area of base \[\times \] Height |
| \[=120\times 50=6000\text{ }c{{m}^{3}}\] |
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