SOLUTION: The Malik's want to build an even tile border around their pool. Their pool is 110 feet long by 40 feet wide. Let x= width of the border. 1.) Write an expression for the area

Algebra ->  Rate-of-work-word-problems -> SOLUTION: The Malik's want to build an even tile border around their pool. Their pool is 110 feet long by 40 feet wide. Let x= width of the border. 1.) Write an expression for the area      Log On


   



Question 716557: The Malik's want to build an even tile border around their pool. Their pool is 110 feet long by 40 feet wide. Let x= width of the border.
1.) Write an expression for the area of the border in terms of x.
2.) If the Malik's have calculated that they will need 936 square feet of tile for the border they chose, how wide is it? Use a strategy other than the quadratic formula.
Thank you so much for whatever help you can provide!

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Total Area minus pool area gives border area.
%28110%2B2x%29%2840%2B2x%29-%28110%29%2840%29= Border Area. That simplifies depending on how far you take it, to Border Area =+4%28x%2B55%29%28x%2B20%29-4400. Note that the pool "area" alone is 110%2A40 sq.ft.

Finding how wide the border if the area must be 936 sq.ft., why would we not use quadratic formula? If we begin with 936=4%28x%2B55%29%28x%2B20%29-4400, when we carry through the steps, ... we obtain without any trouble, the much simpler and good equation of ...
highlight%28x%5E2%2B75-234=0%29.

That does not appear factorable. Why should we use something other than quadratic formula? THE TRICK IS TO FACTOR 234.

234=2%2A3%2A3%2A13, and 3 and 2*3*13 are the same as 3 and 78.
The quadratic equation could be factored into:
highlight%28%28x%2B78%29%28x-3%29=0%29.

The reasonable answer finally is 3 feet width. x=3.