How do I find the dimensions of a rectangle if the length of the rectangle is 1 yard more than twice its width, and the area of the rectangle is 66 yards^2 .
let's use l and w for the variables
l= 2w + 1
lw= 66 yds. ^2
(2w + 1) w= 66
2w^2 + w= 66
2w^2 + w -66 = 0
(2w -11 ) (w + 6 ) = 0
2w= 11 or w= -6
w= 5.5 is positive so this is our answer!!!
and the length = 2w+1 so simply plug in!
l= 2*(5.5)+ 1
l= 12
To find the dimensions of a rectangle when given the length, width, and area, follow these steps:
Step 1: Understand the problem.
Let's denote the width of the rectangle as "w" in yards.
Step 2: Translate the given information into equations.
We know that the length of the rectangle is 1 yard more than twice its width. So, the length can be expressed as: length = 2w + 1.
We also know that the area of a rectangle is given by multiplying its length and width. Therefore, we have the equation: area = length * width.
Step 3: Substitute the values into the equations.
We know that the area is 66 yards^2. So, we can substitute it into the equation:
66 = (2w + 1) * w.
Step 4: Solve the equation.
To solve the equation, we can multiply the terms:
66 = 2w^2 + w.
Rearranging the equation to form a quadratic equation:
2w^2 + w - 66 = 0.
Step 5: Solve the quadratic equation.
By factoring, completing the square, or using the quadratic formula, we find the solutions for w. In this case, the solutions are:
w = -8.25 or w = 4.
Since the width cannot be negative, the width of the rectangle is 4 yards.
Step 6: Find the length.
Using the length equation, we substitute the width we found into it:
length = 2w + 1 = 2 * 4 + 1 = 9 yards.
Step 7: Answer the question.
Therefore, the dimensions of the rectangle are a width of 4 yards and a length of 9 yards.