Question 168154: Swimming space. The length of a rectangular swimming
pool is 2x - 1 meters, and the width is x + 2 meters. Write
a polynomial A(x) that represents the area. Find A(5).
Can someone please help me figure out this problem. Thank you
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let L = length
let W = width
L = 2*x-1
W = x+2
let A = a function of x, such that A(x) = area of the pool = L*W
then:
A(x) = L*W = (2*x-1)*(x+2)
multiplying the 2 factors together, we get:
A(x) = 2*x^2 + 3*x - 2
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in order to find A(5), we have to replace x with 5.
the equation:
A(x) = 2*x^2 + 3*x - 2 becomes:
A(5) = 2*(5)^2 + 3*(5) - 2
simplifying:
A(5) = 2*25 + 15 - 2
A(5) = 50 + 15 - 2
A(5) = 65 - 2
A(5) = 63
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solving from the original factors, we get:
original factors:
L = 2x-1
W = x+2
substituting 5 for x, we get:
L = 2*(5) - 1 = 9
W = 5 + 2 = 7
L*W = 9*7 = 63
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since we get 63 both ways, we know that the equation that we created from the factors is good and that the answer of 63 is also good.
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