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A right prism is based on a triangular base whose perimeter is 26 cm and radius of the in circle of the triangular base is 5 cm. If the volume of the prism is 780 cm3, then find the height of the prism.

A right prism is based on a triangular base whose perimeter is 26 cm and radius of the in circle of the triangular base is 5 cm. If the volume of the prism is 780 cm3, then find the height of the prism. Correct Answer 12 cm

Since the perimeter of the triangular base is 26 cm.

⇒ Semi-perimeter, s = 26/2 = 13 and inradius (r) = 5 cm

inradius of a triangle = A/s

⇒ Area (A) = 13 × 5 = 65 cm2

Volume of prism = (Area of base) × Height

⇒ 780 = 65 × Height

⇒ Height = 780/65 = 12

∴ Height of the prism = 12 cm

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