Question 1198345
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a rectangular piece of artwork is 4 meters wide and 6 meters long 
it is surround by a uniform sidewalk if the area of the sidewalk 
is 39 square meters how wide is the sidewalk?
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Let x be the unknown width of the sidewalk.


Write the area equation for the sidewalk as the difference of the areas of the larger and smaller rectangles

    (4+2x)*(6+2x) - 4*6 = 39  square meters.


To find x, simplify it step by step

    24 + 12x + 8x + 4x^2 - 24 = 39

    4x^2 + 20x - 39 = 0


Use the quadratic formula and accept a positive root, ONLY.


<U>ANSWER</U>.  The wide of the sidewalk is 1.5 m.


<U>CHECK</U>.   (4+2*1.5)*(6+2*1.5) = 7*9 = 63;  63 - 24 = 39  square meters.  ! correct !
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Solved.