SOLUTION: A border of uniform width is built around a rectangular garden that measuers 29ft. by 44ft. The area of the border is 474ft. Find the width of the border.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A border of uniform width is built around a rectangular garden that measuers 29ft. by 44ft. The area of the border is 474ft. Find the width of the border.      Log On


   

Question 1134: A border of uniform width is built around a rectangular garden that measuers 29ft. by 44ft. The area of the border is 474ft. Find the width of the border.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the border be x ft.
Since the outer rectangular should be of dimensions 2x+29 and 2x+44.
The area of the border = Area (outer rectangular -inner rectangular)
We have (2x+29)(2x+44) - 29*44 = 474,
Simplify: 4x^2 + 146 x = 474
Or 2x^2 + 73 x - 237 = 0,
Factoring (2x +79) (x -3) = 0 [Note: 237 =3 * 79]
So, x = 3 or -79/2 (negative ,invalid)
Answer: The uniform width of the border is 3 ft