Question

The bottom and top of a box are rectangles twice as long as they are wide. Find the volume of the box if it is four feet high and has a total surface area of 220 feet squared.

Answer 1

Let x = the width

then

2x = the length

:

The box dimensions: 2x by x by 4

Given the surface area:

2(2x*x) + 2(2x*4) + 2(x*4) = 220

:

4x^2 + 16x + 8x = 220

A quadratic equation:

4x^2 + 24x - 220 = 0

simplify, divide by 4

x^2 + 6x - 55 = 0

Factor

(x+11)(x-5) = 0

The positive solution is what we want here:

x = 5 ft is the width

then

2(5) = 10 ft is the length

:

Find the volume

10 * 5 * 4 = 200 cu/ft is the volume