Mrs. Jacinto ask a carpenter to construct a rectangular bulletin board for her classroom. She told the carpenter that the boards area must be 18 square feet.

1. What are the positive dimensions of the bulletin board? Give at least 2 pairs of possible dimensions.

2. Suppose the length of the board is 7 feet longer than its width. What equation would represent the given equation?

3. How would you describe the equation formulated?

Thank you!

1

Answers

2015-06-07T23:07:31+08:00

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1. The positive dimensions of the board is the factors of 18, since the area of a rectangle is the length*width. The dimensions are: 1ft*18ft, 2ft*9ft, 3ft*6ft

2. We let the width be x, this would make the length x+7.

Area = length * width
18 = (x+7)x This is already the equation you need but I will further simplify.
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.

3. The equation is a quadratic equation.
3 4 3