Box has a rectangular base with a length of 3x+2 and a width of 2x-2, base has a perimeter of 60 centimeters. If the height of the box is x, what is the volume of the box?

Answer 1

Look at the base of your box to solve for x.

The base is a rectangle and has 2 sides that are 3x+2 and 2 sides that are 2x-2. If you add the lengths of all 4 sides, you get a perimeter of 60.

So, 3x + 2 + 3x + 2 + 2x - 2 + 2x - 2 = 60

Combining like terms leaves you with 10x = 60

Therefore x = 6. Which is the height of your box.

To find the volume, find the area of the base and multiply it by the height.

(3x + 2)(2x - 2)(x) = volume

substituting 6 for x, we get

(18 + 2)(12 - 2)(6)

(20)(10)(6) = 1200cm³

Answer 2

Perimeter = twice (one side plus 2nd side)

60=2(3x+2 + 2x-2) = 10x

x = 60/10 = 6 cm

sides = 20, 10, and 6

volume = 20x10x6 = 1200 cm^3