Thinking about area, and width.

Question

Compare the area of the bases. If a base has a greater area, it will take up more space on the shelf.

Base area of Box 1: 3x²

Base area of Box 2: 4x² – x

Which box is likely to occupy more space on the shelf? Explain. Try substituting different values for x.

Answer 1

The best way to do this is to find the value of x where the areas of the two bases are equal:

4x² - x = 3x²

x² - x = 0

x(x-1) = 0

x = 1 and 0

Throw out the x=0 since that means that the boxes have no base area. So the base area are equal when x = 1. One box will have a bigger area when x < 1 and the other box will have a bnigger area when x > 1. To find out, plug in x values on either side of 1, say x = 0,5 and x = 2 to see which box is bigger on which side of x = 1. Ignore negative values of x since you can't have a negative area.