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.

Answer 1

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Volume of right prism = 144 cubic inches

Right prism has a rhombus as a base.

Height of the prism = 6 inches

As we know the formula for "Volume of right prism":

$Volume=\text{Area of base}\times height\\\\144=\frac{1}{2}\times d_1\times d_2\times 6\\\\\frac{144\times 2}{6}=d_1\times d_2\\\\48=d_1\times d_2$

By option we get that

lengths of diagonals could be 6 inches by 8 inches

∵ 8×6 = 48 in²

Hence, Third option is correct.

Answer 2

The answer is C 6in by 8 in.