Question: 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)
Options:
A) $ 6000cm^{3} $
B) $ 6600cm^{3} $
C) $ 5400cm^{3} $
D) $ 9600cm^{3} $
Show Answer
Answer:
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 $ 10cm, $ $ 24cm $ and $ 26cm. $
$ \therefore $ Volume of prism
$ =\frac{1}{2}\times 10\times 24\times 50=6000cm^{3} $