The length of a rectangle is 7 yd more than twice the width, and the area of the rectangle is 99yd^2. Find the dimensions of the rectangle.
Let the width of the rectangle be x yards.
Therefore, the length of the rectangle is 2x + 7 yards.
Given that the area of the rectangle is 99 square yards, we can write the equation:
Area = length * width
99 = (2x + 7) * x
99 = 2x^2 + 7x
2x^2 + 7x - 99 = 0
Now we need to solve this quadratic equation to find the value of x.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 2, b = 7, and c = -99, we get:
x = (-7 ± √(7^2 - 4*2*(-99))) / (2*2)
x = (-7 ± √(49 + 792)) / 4
x = (-7 ± √841) / 4
x = (-7 ± 29) / 4
x = 22/4 or x = -36/4
Since the width cannot be negative, we have:
x = 22/4
x = 5.5
So, the width of the rectangle is 5.5 yards.
Now, the length of the rectangle is:
2 * 5.5 + 7 = 18
Therefore, the dimensions of the rectangle are:
Width = 5.5 yards
Length = 18 yards