HI I NEED HELP PLEASE
Mrs. Jacinto asked a carpenter to construct a rectangular bulletin board for her classroom. She told the carpenter that the board's area must be 18 square feet.

1. Suppose the length of the board is 7 ft. longer than it's width what equation would represent the given situation?

Please explainnnn :)

1

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2015-06-03T20:03:43+08:00

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We let the width be x, and this would make the length be x+7 so:
Area = length * width
18 = x(x+7)
So we simplify this:
18 = x²+7x
0 = x²+7x-18

Method 1: Guess and Check
We look for two numbers with a product of 18 and an absolute difference of 7 so we check the factors of 18:
18 - 1 =17  X
9 - 2 = 7  √
6 - 3 = 3  X
So we have:
0 = (x+9)(x-2)
We then equate each to 0:
If x+9 = 0              If x-2 = 0
x = -9                    x = 2
Since we cannot have a negative length, the width is 2 ft and the length is 2+7 = 9ft.

Method 2: Quadratic Formula
x = -7 ± √(7²+72) = -7 ± √121 = -7 ± 11 = 2 or -9
              2                   2             2
Then again we cannot have a negative length so the width is 2ft and the length is 9 ft

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