Question

Modeling with Mathematics:

A square-shaped parking lot with 100-foot sides is reduced by x feet on one side and extended by x feet on an adjacent side.

a) The area of the new parking lot is represpresented by (100+ x)(100 – x).
Find this product.

b) Does this area of the parking lot increase, decrease, or stay the same? Explain your thinking. (You can use example values for x to help explain.)

Answer 1

a) Difference of squares:

`10000 - {x}^(2)`

b) The area of the parking lot decreases because x^2 is subtracted from 10,000.

`10000 - {1}^(2) = 10000 - 1 = 9999`

`10000 - {2}^(2) = 10000 - 4 = 9996`