Question 1197581: The area of a rectangular fountain is (x^2 + 11x + 18)
square feet. A 1-foot walkway is built around the
fountain. Find the dimensions (in factor form) of the
outside border of the walkway.
(please explain your work so i can understand how to do these types of problems! thanks in advance!)
Answer by ikleyn(52847)   (Show Source):
You can put this solution on YOUR website! .
The area of a rectangular fountain is (x^2 + 11x + 18)
square feet. A 1-foot walkway is built around the
fountain. Find the dimensions (in factor form) of the
outside border of the walkway.
(please explain your work so i can understand how to do these types of problems! thanks in advance!)
~~~~~~~~~~~~~~~
Factor this trinomial
x^2 + 11x + 18 = (x+9)*(x+2).
It says you that the dimensions of the rectangular fountain are,  ,
(x+9) feet and (x+2) feet.
The 1-foot uniform wide walkway increases the dimension to (x+11) and (x+4) feet.
It is what you want to know.
Solved and explained.
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Why I said "probably", highlighted by red ?
Because the problem can be treated in different way, as if one dimension is 1 unit,
while the other dimension is the trinomial x^2 + 11x + 18.
Then the answer is, SURELY, totally different.
But from the context, the solution, which I placed at very beginning, is expected.
Although, from the other side, determining the expectations of another person is, probably and often, a transcendent task.
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