A right prism has a rhombus as a base. The height of the prism is 6 inches and the volume is 144 cubic inches. Which could be the lengths of the diagonals of the rhombus?

The base area is the prism’s volume divided by its height: 144 ÷ 6 = 24 square inches. A rhombus’s area is half the product of its diagonals, so the diagonals must have a product of 2 × 24 = 48. The pair 6 inches by 8 inches has product 48, so it gives the required area.

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