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

Volume = base area × height, so base area = 144/6 = 24 in².
For a rhombus, area = (d1·d2)/2, so d1·d2 = 48.
Check options: 2·12=24, 4·11=44, 6·8=48, 8·9=72.

Thus 6 in by 8 in.