SOLUTION: The dimensions of a rectangle fish pond are 6m and 9m.The pond is surrounded by a cement walk of uniform width. a.find the area of walk is equal to the area of the fish pond,write

Algebra ->  Rectangles -> SOLUTION: The dimensions of a rectangle fish pond are 6m and 9m.The pond is surrounded by a cement walk of uniform width. a.find the area of walk is equal to the area of the fish pond,write      Log On


   

Question 1074313: The dimensions of a rectangle fish pond are 6m and 9m.The pond is surrounded by a cement walk of uniform width.
a.find the area of walk is equal to the area of the fish pond,write the equation in the simplified form showing this information.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x, the uniform width of walkway

%286%2B2x%29%289%2B2x%29, the combined area of upper surface of pond and the cement walkway


Walkway area and fish pond area are equal.
%286%2B2x%29%289%2B2x%29=2%2A6%2A9


54%2B18x%2B12x%2B4x%5E2-2%2A6%2A9=0
27%2B9x%2B6x%2B2x%5E2-6%2A9=0
2x%5E2%2B15x%2B27-54=0
highlight_green%282x%5E2%2B15x-27=0%29
or as factored,
highlight_green%28%282x-3%29%28x%2B9%29=0%29

The sensible result is x=3%2F2=1.5%2Ameter
Walkway is 1 and half meter wide.