Answer:
The length of the rectangle is 11 yards, the width of the rectangle is 6 yards.
Explanation:
1. Let's check the information given to resolve the question:
Width of the rectangle = x
Length of the rectangle = 2x - 1 (Length of the rectangle is 1 yd more than twice the width)
Area of the rectangle = 66 square yards
2. Let's find the value of the length and the width
Area of the rectangle = Length of the rectangle * Width of the rectangle
66 = x (2x - 1)
66 = 2x² - x
0 = 2x² - x - 66 (Subtracting 66 at both sides)
This is a quadratic equation and the formula to solve it is this:
x = [ - b +/- √ (b² - 4ac)/2a]
x = - [- (- 1) +/- √(1 ² - 4 (2) (-66))/2(2)]
x = - [1 +/- √(1 + 528)/4]
x = - [1 +/- √529)/4]
x = - [1 +/- 23/4]
x₁ = 24/4 = 6
x₂ = -22/4 = -5.5
We will take the value of x₁ because x₂ is negative and the width can't be negative.
Width of the rectangle = 6 yards
Length of the rectangle = 2x - 1 = 2(6) -1 = 12 -1 = 11 yards
The length of the rectangle is 11 yards, the width of the rectangle is 6 yards.