The length of the diagonal of a rectangular box with length l , width w , and height h , is given by . Find the length of the diagonal of a rectangular box that is 5 feet wide, 8 feet long, and 12 feet high. Round your answer to the nearest tenth of a foot.
A) The length of the diagonal is 239.1 feet.
B) The length of the diagonal is 233.0 feet.
C) The length of the diagonal is 14.6 feet.
D) The length of the diagonal is 15.3 feet.
E) The length of the diagonal is 14.2 feet.

Question

The length of the diagonal of a rectangular box with length l , width w , and height h , is given by  . Find the length of the diagonal of a rectangular box that is 5 feet wide, 8 feet long, and 12 feet high. Round your answer to the nearest tenth of a foot. 
A) The length of the diagonal is 239.1 feet. 
B) The length of the diagonal is 233.0 feet. 
C) The length of the diagonal is 14.6 feet. 
D) The length of the diagonal is 15.3 feet. 
E) The length of the diagonal is 14.2 feet.

Quizplus · Accepted Answer

Using the formula given, we have:

diagonal = sqrt(l^2 + w^2 + h^2)

Substituting l = 8, w = 5, and h = 12, we get:

diagonal = sqrt(8^2 + 5^2 + 12^2)

diagonal = sqrt(64 + 25 + 144)

diagonal = sqrt(233)

diagonal ≈ 15.3 feet (rounded to the nearest tenth)

Therefore, the best choice is D, which is the closest option to 15.3.

The Length of the Diagonal of a Rectangular Box with Length