The perimeter of the triangular base of a right prism is 60 cm. The sides of the base are in the ratio 5 : 12 : 13. If the prism height is 60 cm, find the volume of the prism (in cm^3).

Introduction / Context:For a right prism, the volume equals the area of the base times the prism height. The 5:12:13 ratio indicates a Pythagorean triple (right triangle), simplifying the base area calculation.

Given Data / Assumptions:

• Perimeter = 60 cm; ratio 5:12:13 → sides 10 cm, 24 cm, 26 cm.
• Right triangle legs: 10 cm and 24 cm; hypotenuse 26 cm.
• Prism height H = 60 cm.

Concept / Approach:Base area A = (1/2) * (product of legs). Then volume V = A * H.

Step-by-Step Solution:

Verification / Alternative check:5-12-13 confirms right angle; area via Heron also yields 120 cm^2, validating result.

Why Other Options Are Wrong:6000, 6600, 5400 cm^3 do not match the exact base area times height.

Common Pitfalls:Using hypotenuse in the area formula; mis-scaling side lengths from the ratio; mistaking perimeter for semi-perimeter in Heron’s formula.

Final Answer:7200 cm3