A certain rectangular prism has a height of h inches. It has a width that is 3 less than its height and a length that is 4 inches more than its height. If the area of the base is 60 in^2, what is the volume in cubic inches. (Answer is 480, but I don't understand the process)

Question

anonymous · Answer

Willing to give a medal or whatever if someone tells me how to!

anonymous · Answer

Help please

hurgleman · Answer

You know that the base is 60
60 = l * w
you know that width is height - 3 inches
w = h-3

you know that length is h+4 inches
l=h+4

So now you plug in length and width with those equations.
60 = (h+4) * (h-3)

Foil the expressions.
60 = h^2 + h -12
expressing h as x
60=x^2+x-12   or 72=h^2+h

Set one side to 0
0 = h^2 + h - 72
Then, you can use the quadratic formula to identify what 2 factors this breaks down to.
$$(-1 +\sqrt{1-(4*-72})/2$$
so (-1+- 17)/2
your answers are -9 or 8.
h = 8 or h=-9
Since it's volume, you can't use a negative number, so h=8

hurgleman · Answer

From there you can plug in 8 to anywhere that H is.
V = 8 * (8-3) * (8+4) = 480
480 = 8 * 5 * 12