A rectangular box has a length of 8 feet and a width of 2 feet. The length of the three-dimensional diagonal is 10 feet. What is the height of the box?

The answer is 4√2 ft i. e (5.66ft)

Step-by-step explanation:

The length, width and height of a rectangular box are all perpendicular.

This means the length of the diagonal is the Pythagorean distance of the three sides.

So, square of diagonal = L^2 + W^2 + H^2

So,

100 = 64 + 4 + H^2

H^2 = 100 - 68 = 32

H = √32 = 4√2 = 5.66ft