Linear Equation Word Problem

Question

A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 18 ft, its width is 8ft, and its surface area is 496 ft^2. Assume that the given surface area includes that of the top lid of the box. 

Answer 1

The surface area of a rectangular box is the sum of the areas of the flat rectangular faces of the box. The height is the vertical side of the box.  So the other sides are the length and width.  Try to picture a box in your head, or you can draw it on paper.

 

Let x = length

Let y = width

Let h = height

 

Using these variables, we can write an equation that represents the surface formula.

 

A = 2(area of bottom face) + 2(area of front face) + 2(area of side face)

 

A = 2xy + 2xh + 2yh

 

 

This is general equation for surface area.  All we need to do is plug in the known values into it and solve for h.

 

496 = 2(18)(8) + 2(18)h + 2(8)h

 

496 = 288 + 36h + 16h

 

 

Now it comes down to simple algebra.  Isolate the h terms and solve for h from there.

 

208 = 52h

 

 

Divide both sides of the equation by 52 to get your height.  I let you finish up here.