A box shaped like a right rectangular prism measures 8 inches by 6 inches by 5 inches. What is the length of the interior diagonal of the prism to the nearest hundredth?
The interior diagonal of a right rectangular prism can be found using the Pythagorean theorem. Let the length of the diagonal be d.
Using the Pythagorean theorem, we have:
d^2 = 8^2 + 6^2 + 5^2
d^2 = 64 + 36 + 25
d^2 = 125 + 36
d^2 = 161
Taking the square root of both sides, we get:
d = √161
d ≈ 12.69
Therefore, the length of the interior diagonal of the prism is approximately 12.69 inches.