Question

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? 2 in. by 12 in. 4 in. by 11 in. 6 in. by 8 in. 8 in. by 9 in.

Explanation:

Step1: Find base area of prism

Volume formula: $V = B \times h$, so $B = \frac{V}{h}$
$B = \frac{144}{6} = 24$ square inches

Step2: Relate to rhombus area

Rhombus area: $B = \frac{d_1 \times d_2}{2}$, so $d_1 \times d_2 = 2B$
$d_1 \times d_2 = 2 \times 24 = 48$

Step3: Check option products

Calculate product for each option:

• $2 \times 12 = 24$
• $4 \times 11 = 44$
• $6 \times 8 = 48$
• $8 \times 9 = 72$

Answer:

6 in. by 8 in.