Final answer:
To find the dimensions of the rectangle with an area of 27 square feet, where the length is 3 feet less than twice the width, we solve the quadratic equation 2W^2 - 3W - 27 = 0, resulting in a width of 4.5 feet and a length of 6 feet.
Step-by-step explanation:
Finding the Dimensions of a Rectangle Given Its Area
The question involves a rectangle where the length is 3 feet less than twice the width, and the area is 27 square feet. To solve for the dimensions of the rectangle, we can set up a system of equations based on the information provided:
Let W represent the width of the rectangle. Therefore, the length L can be represented as 2W - 3 feet. Knowing that area (A) is equal to length times width (A = L × W), we can set up an equation using the area of the rectangle: 27 sq ft = (2W - 3) × W.
The equation simplifies to a quadratic equation: 2W^2 - 3W - 27 = 0.
After factoring or using the quadratic formula, we find that the width W is 4.5 feet and the length L is 2×4.5 - 3 which equals 6 feet. Therefore, the dimensions of the rectangle are a width of 4.5 feet and a length of 6 feet.