SOLUTION: What is the length of the diagonal of a rectangular box with a length of 5cm, width of 4cm, and height of 2cm?

Question 933448: What is the length of the diagonal of a rectangular box with a length of 5cm, width of 4cm, and height of 2cm?
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

the length of the diagonal of a rectangular box with a:
length of , width of , and height of
The base of the box is a rectangle of sides and . Thus its diagonal , (of the base only), satisfies by the Pythagorean theorem.

...if , and we will have

Next consider the rectangle formed by this diagonal, the diagonal above it (parallel to it), and the two vertical sides connecting the two diagonals. This rectangle has the diagonal connecting opposite sides of the box.
Since the dimensions of this rectangle are and , again by the Pythagorean theorem , then we have

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