Using quadratics to find the dimensions of a rectangle

Question

A rectangular garden measures 24m by 32m. a path of uniform width is built all around the outside of the garden. The total area of the path and garden is 1540m^2. Find the width of the path.

please show the method used to solve this to get an answer of either 3.49m by 43.0m or 21.5m by 6.97m.

 

Thank you!

Answer 1

(24+2x)(32+2x) = 1540

divide both sides by 4 to simplify

(12 +x)(16+x) = 385

192 + 28x +x^2 = 385

x^2 +28x - 193 = 0

x = about 5.72308 or -33.72308 (ignore the negative solution)

walkway is about 5.7 meters wide