Algebra II problem

Question

You have a garden that measures 15ft by19ft. You want to put a sidewalk around the garden but are not sure how wide to make it. Determine how wide the sidewalk should be when the total area of the garden and sidewalk is 480 square feet. Show work

Answer 1

Hi Elizabeth

This is a fun problem but there is a little trick at the end you have to be careful about. Your garden is 15 x 19 and if you put a sidewalk around that rectangle then you increase the sides to 15+x and 19+x. You know the total area so FOIL that (x+15)(x+19)=480

The equation after using algebra is x² +34x - 195 = 0 and if you factor your factors are (x-5) and (x+39). The only possible answer is 5 because -39, or any negative number, doesn't apply when we are talking about a measurement of an object.

Here is the trick you must remember, the extension is 5 in total, not 5 on each side, so your sidewalk is actually 2 1/2 feet wide. But now your area is 20 x 24 and that does multiply to 480 so we know we did the math correctly.

All the best,

Lori