To find the length of the longest diagonal of a rectangular prism, you can use the three dimensions (length, width, and height) as the three sides of a right triangle. Then, you can apply the Pythagorean theorem to calculate the diagonal (hypotenuse).
In this case:
Length (L) = 5 inches
Width (W) = 8 inches
Height (H) = 10 inches
Let D be the length of the longest diagonal:
D² = L² + W² + H²
D² = 5² + 8² + 10²
D² = 25 + 64 + 100
D² = 189
Now, take the square root of 189 to find D:
D = √189 ≈ 13.74 inches
So, the length of the longest diagonal of the rectangular prism is approximately 13.74 inches.