How do you find the height of a rectangular box when length is 7 m and width is 5 m and diagonal length 10m?

Answer 1

I guess the diagonal length given is from one corner of the box to the opposite corner reached by traversing one length side, one edge side and one height side.

Using Pythagoras, the length of the diagonal of the base (length by width) can be found.

Using this diagonal and the height of the box, the diagonal from corner-to-opposite-corner of the box can be found using Pythagoras. However, as this [longer] diagonal is know, the height can be found by rearranging this last use of Pythagoras:

Diagonal_base2 = length2 + width2

Diagonal_box2 = diagonal_base2 + height2

⇒ height = √(diagonal_box2 - diagonal_base2 )

= √(diagonal_box2 - (length2 + width2))

= √(diagonal_box2 - length2 - width2)

Now that the formula has been derived, plugging in (substituting) the various lengths will allow the height to be calculated.