The dimensions of a box that is a rectangular prism are 3 inches, 4 inches, and 6 inches. What is the length of the diagonal to the nearest tenth of an inch?

7.8

6.7 To find the length of the diagonal, we can use the Pythagorean Theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the rectangular prism are 3 inches and 4 inches, so we can calculate the length of the diagonal as follows:

Step 1: Square the lengths of the two sides.
3^2 = 9
4^2 = 16

Step 2: Add the squared lengths together.
9 + 16 = 25

Step 3: Take the square root of the sum.
√25 = 5

Therefore, the length of the diagonal is 5 inches.

To express the length to the nearest tenth of an inch, round the answer to one decimal place. In this case, the length of the diagonal is already a whole number, so when rounded to one decimal place, it remains 5.0 inches.