SOLUTION: 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?

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

Then

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:

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:

Then eliminate the factor common to both numerator and denominator:

Done.

John

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
A(x) = x^2 +5x +6
.
a(5) = (5)^2 + 5(5) +6 = 56
.
A(x) = x^2 +5x +6 = 1/2 ( h) (l) = (1/2) (x+3) h,,,,,,,area of triangle = 1/2 base * height
.
{ (x+3)(x+2) } / (1/2) ( x+3) = 2(x+2) = h
.
check
.
A(5) = 56, (x+3)= 8,, A = 1/2 * 8 * h = 56,,,,,h= 112/8 = 14
.
h=2(x+2) = 2 (5+2) =14,,,,,,ok
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