The width of a rectangle is the length minus 8 units. The area of the rectangle is 9 square unitsWhat is the length, in units, of the rectangle?
Let the length of the rectangle be x units.
Given that the width of the rectangle is the length minus 8 units, the width of the rectangle would be x - 8 units.
The formula for the area of a rectangle is length times width. Therefore, the area of the rectangle can be expressed as:
x(x - 8) = 9
x^2 - 8x = 9
x^2 - 8x - 9 = 0
Now, we need to solve this quadratic equation for x.
Using the quadratic formula:
x = (-(-8) ± √((-8)^2 - 4*1*(-9))) / 2*1
x = (8 ± √(64 + 36)) / 2
x = (8 ± √100) / 2
x = (8 ± 10) / 2
x = (8 + 10) / 2 = 18 / 2 = 9
x = (8 - 10) / 2 = -2 / 2 = -1
Since the length of a rectangle cannot be negative, the length of the rectangle is 9 units.