SOLUTION: 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?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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?       Log On


   

Question 1198345: 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?


Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~ 

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.


ANSWER.  The wide of the sidewalk is 1.5 m.


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

Solved.