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A right triangular prism stands as a display unit. Its triangular cross-section is a right triangle with legs of 5 cm and 12 cm, and the prism's length is 20 cm. Find the ratio of the area of its largest rectangular face to that of its smallest rectangular face.

1. 5 : 3
2. 12 : 5
3. 13 : 5
4. 13 : 12

Correct answer: 13 : 5

Solution

The hypotenuse is sqrt(5^2 + 12^2) = 13 cm. The three rectangular faces have areas 5x20, 12x20, and 13x20. Largest to smallest is (13x20):(5x20) = 13:5.

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