Question

select the correct answer. an online retailer is shipping a shower curtain pole that is 13 feet long. their largest box is in the shape of a rectangular prism that is 10 ft × 9 ft × 8 ft. will the pole fit in the box? a. no, because the longest diagonal of the box is 12.1 feet long. b. no, because the longest diagonal of the box is 12.8 feet long. c. yes, because the longest diagonal of the box is 15.7 feet long. d. yes, because the longest diagonal of the box is 13.5 feet long.

Explanation:

Step1: Recall diagonal formula for rectangular prism

For a rectangular prism with length $l$, width $w$, and height $h$, the length of the space - diagonal $d$ is given by $d=\sqrt{l^{2}+w^{2}+h^{2}}$. Here, $l = 10$, $w=9$, and $h = 8$.

Step2: Calculate the diagonal length

$d=\sqrt{10^{2}+9^{2}+8^{2}}=\sqrt{100 + 81+64}=\sqrt{245}\approx15.7$ feet.
Since the length of the pole is 13 feet and the longest diagonal of the box is approximately 15.7 feet, the pole will fit.

Answer:

C. Yes, because the longest diagonal of the box is 15.7 feet long.