Question

The perimeter of the triangular base of a right prism is 60 cm and the sides of the bases are in the ratio of 5:12:13 and height of the prism is 50 cm . Find it's volume?

1. 6000 cm³
2. 6600 cm²
3. 9000 cm³
4. NOT

Answer 1

Correct Answer - Option 1 : 6000 cm³

GIVEN:

 Perimeter of the base = 60 cm and height of prism = 50 cm , sides ratio = 5:12:13

FORMULA USED:

Volume of Prism = (Base Area) × Height

CALCULATION:

perimeter of triangular base =  \(5x + 12x + 13x = 60 ⇒ 30x = 60 ⇒ x = 2\) 

⇒ sides of the base = \(5 × 2 = 10\;,\;12 × 2 = 24\;,\;13 × 2 = 26\) 

⇒ Area of Right triangular base =\(\frac{1}{2} \times Base \times Height = \frac{1}{2} \times 10 \times 24 = 120\;c{m^2}\) 

∴ volume of prism = 120 × 50 = 6000 cm³