SOLUTION: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set aroung the edge. If the remaining garden area is 400 ft^2, what is the width of the path?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set aroung the edge. If the remaining garden area is 400 ft^2, what is the width of the path?      Log On


   

Question 84427: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set aroung the edge. If the remaining garden area is 400 ft^2, what is the width of the path?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the length of the remaining garden area is the original length minus twice the width of the path, similarly with the original width ... let x=width of path

(30-2x)(20-2x)=400 ... 600-100x+4x^2=400 ... x^2-25x+50=0 ... x=%2825+%2B-+sqrt%2825%5E2-4%2A1%2A50%29%29%2F%282%2A1%29 ... x=%2825+%2B-+sqrt%28425%29%29%2F2

x=12.5 +- 2.5(sqrt(17)) ... x approximately equals 22.81 and 2.19

the 22.81 is not realistic based on the garden size