SOLUTION: A grassy space is 6 feet by 8 feet. The town wants to add a walking track around this space. If the total area is to be 71 square feet, what should be added to each side of the gra

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A grassy space is 6 feet by 8 feet. The town wants to add a walking track around this space. If the total area is to be 71 square feet, what should be added to each side of the gra      Log On


   

Question 1092105: A grassy space is 6 feet by 8 feet. The town wants to add a walking track around this space. If the total area is to be 71 square feet, what should be added to each side of the grassy space? (Round to the nearest hundredth.)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The area of the walking track is the difference of areas of the larger rectangle and the smaller rectangle.


The dimensions of the larger rectangle are 6+2x and 8+2x, where x is (unknown) width of the walking track.


Your equation is

(6+2x)*(8+2x) - 6*8 = 71.


Simplify and solve for x.


4x^2 + 28x - 119 = 0.


Now apply the quadratic formula and find the positive solution of this quadratic equation.


See the lesson
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
in this site and find there examples/samples of solved problems of this type.