derived the formulafor the diagonal of a rectangular solid,

square root of l^2 + w^2+ h^2

Solution:

The length of rectangel solid:l

The width of rectangel solid:w

The height of rectangel solid:h

So the diagnoal of the base is sqrt(l^2+ w^2)

The diagnoal of the base, the height and the diagonal of a rectangular solid form a right triangle, so

[sqrt(l^2+ w^2)]^2 + h^2 = (Diagonal of rectangular solid)^2

So

the diagonal of a rectangular solid = sqrt(l^2 + w^2+ h^2)