What is the volume of the rectangular box with a height of 5 length of 7 and a diagonal of 6?

Answer 1

Volume is a physical variable, thus in order to evaluate the volume it is needed to give measurements units to the sides dimensions. For example, if length is in inch, height in meters and diagonal in cm, you have to convert all in the same measurement unit before proceeding.

Let us assume that all the measures are in meters.

In this case, we can apply the fact that the square diagonal (d) is the sum of the squares of all the sides (x, y and z). Thus

d2 = x2 + y2 + z2

From this equation we see that, if the numbers are all in the same unit of measure, the diagonal cannot be smaller than one side, thus it does not exist a rectangular box with a side equal to 7 m and a diagonal equal to 6 m.