Final answer:
The approximate measurement of the diagonal of the cube with a length of 5 feet is approximately 8.66 feet.
Step-by-step explanation:
The measurement of the diagonal of a cube can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its other two sides.
In this case, the diagonal of the cube is the hypotenuse of a right triangle formed by the length, width, and height of the cube. Since a cube has equal sides, we can consider each side as a leg of the right triangle.
Using the Pythagorean theorem, we can find the length of the diagonal:
d = sqrt(l^2 + w^2 + h^2)
Substituting the side length of the cube as 5 feet:
d = sqrt(5^2 + 5^2 + 5^2)
d = sqrt(75)
d ≈ 8.66 feet