Explanation:
Let's denote the width of the rectangle as "w".
According to the problem statement, we know that the length of the rectangle is 7 yards more than twice the width.
Therefore, the length of the rectangle can be expressed as:
length = 2w + 7
We also know that the area of the rectangle is 99 square yards.
Therefore, we can set up an equation:
area = length x width
Substituting the expressions for length and area, we get:
99 = (2w + 7) x w
Expanding the expression on the right-hand side, we get:
99 = 2w^2 + 7w
Moving all the terms to one side, we get:
2w^2 + 7w - 99 = 0
We can solve this quadratic equation using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = 7, and c = -99.
Plugging in these values, we get:
w = (-7 ± sqrt(7^2 - 4(2)(-99))) / 2(2)
w = (-7 ± sqrt(1093)) / 4
The two solutions for w are:
w ≈ 5.5 or w ≈ -9
Since the width of the rectangle cannot be negative, we can discard the negative solution.
Therefore, the width of the rectangle is approximately 5.5 yards.
Using the expression for the length that we derived earlier, we can find the length of the rectangle:
length = 2w + 7
length ≈ 2(5.5) + 7
length ≈ 18
Therefore, the dimensions of the rectangle are approximately:
width = 5.5 yards
length = 18 yards