Rectangle in a rectangle

Question

A concrete walk of uniform width around a rectangular garden that measures 24 by 40 feet is to be built. You have available concrete mix of 272 square feet. How wide should the concrete walk be to use up all the concrete mix?

 

They do give a graph.

Answer 1

A = area of total garden plus sidewalk

A = 24*40+272 = 960 + 272

x = width of sidewalk

A = (x+24)(x+40) = x^2 + 64x + 960 = 960 + 272

x^2 + 64x -272 = 0

(x+68)(x-4) = 0

thus x = - 68 or 4

Answer: sidewalk of 4 feet