Question 199746: area of a sale. The area of in square meters for a triangular sale is given by A(x)=x^2+5x+6 Find A(5), if the hignt of the sail is x+3 meters, then what is the lenght of the sail?
Found 2 solutions by solver91311, RAY100:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I'm unsure how to measure the area of a 'sale'. Perhaps it is the area of the floor surface in a store where a sale is being held. However, I suspect you meant 'sail' since that is the word you used later in the problem, and I will proceed on that assumption. Furthermore, I have no idea what the 'hignt' or 'lenght' of a sail (or a sale for that matter) is. I'm going out on a limb here and will assume you meant 'height' and 'length'. The point of this part of my lesson is that if I am going to take the time to help you, you are obligated to take the time to communicate correctly and completely. Enough said about that.
If
 = x^2 + 5x + 6)
Then
 =(5)^2 + 5(5) + 6)
The arithmetic is left as an exercise for the student.
The area of a triangle is given by:
Therefore, the measure of the base (your length), given the area and the height, is given by:
Since the area as a function of  is the function  ) , the measure of the base, which is equivalent to the length that is the answer to this problem can be determined by:
}{x + 3})
There are two ways to proceed from here. One, you could use polynomial long division to obtain the quotient  . The other way, and much simpler, is to simply factor the polynomial in the numerator:
(x + 3)}{x + 3})
Then eliminate the factor common to both numerator and denominator:
 = 2x + 4)
Done.
John
Answer by RAY100(1637)  (Show Source):
You can put this solution on YOUR website! A(x) = x^2 +5x +6
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a(5) = (5)^2 + 5(5) +6 = 56
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A(x) = x^2 +5x +6 = 1/2 ( h) (l) = (1/2) (x+3) h,,,,,,,area of triangle = 1/2 base * height
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{ (x+3)(x+2) } / (1/2) ( x+3) = 2(x+2) = h
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check
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A(5) = 56, (x+3)= 8,, A = 1/2 * 8 * h = 56,,,,,h= 112/8 = 14
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h=2(x+2) = 2 (5+2) =14,,,,,,ok
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