Question

A rectangle parking space is m feet wide and n feet long. in the new design for the parking lot, each space will have its width increased by 1 foot and its length by 20%.

a.) write a polynomial to represent the area of the new parking space.
b.) shoshanna says that the area of each new parking space is 20% larger than the area of the old parking space. is this correct? use the polynomial you wrote in part a to explain why or why not.

Answer 1

a) width will be m + 1 and length will be 1.2n

so area of new space = 1.2n(m + 1) = 1.2mn + 1.2n answer

b) area of the old parking lot = mn

ratio of new lot to the old = (1.2mn + 1.2n) / mn = 1.2 + 1.2/m

If the new lot was 20% larger then its area would be 1.2mn and the ratio would be 1.2 which is not the same as the ratio just worked out, so shoshanna was wrong.