Question 1020309
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A path of uniform width surrounds a rectangular garden that is 5 m wide and 12 m long. 
The area of the path is 168 m squared. Find the width of the path.
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Your equation is 

(5+2x)*(12+2x) - 5*12 = 168,

where x is an unknown width of the path. 
The equation's left side is the difference between the areas of the larger rectangle and the area 
of smaller rectangle which represents the garden.
The right side is the given area of the surrounding path.

Simplify the equation:

{{{4x^2 + 10x + 24x + 60 - 60}}} = {{{168}}},   or

{{{4x^2 + 34x - 168}}} = {{{0}}}.

Use the quadratic formula to find the roots.

The only root which fits is positive x = 3.5.

Check: (5+2*3.5)*(12+2*3.5) - 60 = 12*19 - 60 = 168.   (OK!)

<U>Answer</U>. The width of the path is 3.5 m.
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