SATHEE: Quantitative Aptitude Ques 2177

Quantitative Aptitude Ques 2177

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) (a) $ 6000cm^{3} $

B) $ 6600cm^{3} $

C) (c) $ 5400cm^{3} $

D) $ 9600cm^{3} $

Show Answer

Answer:

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=6000cm^{3} $

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