What is the length of the diagonal for the given rectangular prism to the nearest whole unit?

A rectangular prism is shown. A bold yellow line extends from the upper rear vertex to the lower front right vertex. To the right of the prism the text 'Length equals 6 centimeters', 'Width equals 5 centimeters', and 'Height equals 9 centimeters' is displayed.
A. 8 cm
B. 10 cm
C. 11 cm
D. 12 cm

1 answer

To find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle whose legs are the length, width, and height of the prism.

Using the Pythagorean theorem, we have:

diagonal^2 = length^2 + width^2 + height^2
diagonal^2 = 6^2 + 5^2 + 9^2
diagonal^2 = 36 + 25 + 81
diagonal^2 = 142
diagonal ≈ 11.9

Rounding to the nearest whole unit, the length of the diagonal is 12 cm.

Therefore, the answer is D. 12 cm.