what is the height of the solid in terms of x

Question

The volume of a rectangular solid is x³−9x cubic inches.

If the area of the base of the solid is x²+ x − 6 square inches, what is the height of the solid in terms of x?

Answer 1

Hello Khalid,

volume = area * height

so height = volume/ area = (x³−9x) / ( x²+ x − 6)

both area and volume can be factored so let’s try that:

volume = x³−9x = x(x² - 9) = x (x-3)(x+3)

area = x²+ x − 6 = (x-2)(x+3)

so: height = x (x-3)(x+3) / (x-2)(x+3)

you should be able to see that there’s (x+3) in the numerator and the denominator, so it cancels out and leaves you with:

height = x (x-3)/(x-2)