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.
