Final answer:
To find the dimensions of the rectangle, we set up an equation using the given information. Solving the equation gives us the width and length of the rectangle.
Step-by-step explanation:
To solve this problem, we need to set up an equation using the given information. Let's assume that the width of the rectangle is 'w'. According to the problem, the length of the rectangle is 1 more than twice the width, so length = 2w + 1.
The area of a rectangle is given by the formula: Area = length × width. We are told that the area of the rectangle is 66m², so we can write the equation as:
(2w + 1) × w = 66
Simplifying this equation, we get:
2w² + w - 66 = 0
Now we can solve the quadratic equation to find the values of 'w'. By factoring or using the quadratic formula, we find that 'w' can be either -11 or 3.5. Since width cannot be negative, we take 'w' = 3.5.
So, the dimensions of the rectangle are: Width = 3.5m, Length = 2 × 3.5 + 1 = 8m.