The length of a rectangle is 7 yd more than double the width, and the area of the rectangle is 99 yd^2. find the dimensions of the rectangle.
L= 2w+7 (equation for length width would just be w)
A= 99 yd^2 (what you are given)
A= LW (Equation for area)
99= W(2W+7) (substitution)
99= 2W^2+7W (distributed)
2W^2+7w-99 (factor out)
(2W-11)(W+9)
W= 11/2, -9 (rectangle can't have - dimensions so 11/2)
L=2(11/2)+7 = 18
L=18 and W= 11/2
width --- x
length = 2x+7
x(2x+7) = 99
2x^2 + 7x - 99 = 0
Solve for x using your favourite method, reject the negative answer
hint: the solution is a rational number
Width = W.
Length = 2W + 7
W*(2W+7) = 99.
2w^2 + 7w - 99 = 0,
Use Quadratic formula to find W.
W = (-7 +- sqrt(49 + 792))/4 = 5.5, and -9 yds. Use the positive value.
To find the dimensions of the rectangle, we can use the information given about the length and width and the formula for calculating the area of a rectangle.
Let's assume the width of the rectangle is "x" yd.
According to the given information, the length is 7 yd more than double the width. So, the length would be 2x + 7 yd.
The formula for finding the area of a rectangle is length multiplied by width: Area = Length * Width.
We are told that the area of the rectangle is 99 yd^2. So, we can set up the equation:
99 = (2x + 7) * x
Now let's solve this equation to find the value of x.
Expanding the equation:
99 = 2x^2 + 7x
Reordering the equation:
2x^2 + 7x - 99 = 0
Now we can factor this quadratic equation, use the quadratic formula, or complete the square to find the value(s) of x.
Factoring the quadratic equation:
(2x - 9)(x + 11) = 0
Setting each factor to 0 and solving for x:
2x - 9 = 0 or x + 11 = 0
Solving for x:
2x = 9 or x = -11
x = 9/2 or x = -11
Since the dimensions cannot be negative, we take x = 9/2 (2.5) as the width.
Now, substitute the value of x into the equation for the length:
Length = 2x + 7 = 2(9/2) + 7 = 9 + 7 = 16
Therefore, the dimensions of the rectangle are:
Width = 9/2 (or 4.5) yd
Length = 16 yd