Final answer:
To solve for the rectangle's dimensions, we set up a quadratic equation, 2W² + 3W - 54 = 0, derived from the area of the rectangle and the relationship between its length and width. After finding the width (W) by factoring or applying the quadratic formula, we can calculate the length (L) using the equation L = 2W + 3.
Step-by-step explanation:
To solve the word problem using a quadratic equation, we need to find the dimensions of a rectangle given that its area is 54 ft² and the length (L) is 3 ft more than twice the width (W). We express this information in two equations: L = 2W + 3 and Area = L × W.
Substituting the first equation into the second gives us: Area = (2W + 3) × W. Since we know the area is 54 ft², we can write the equation as 54 = (2W + 3)W. Expanding this gives us a quadratic equation: 54 = 2W² + 3W. Now, we can rearrange the equation to standard form: 2W² + 3W - 54 = 0.
To find the width (W), we factor the quadratic equation or use the quadratic formula. Once we have the value of W, we can find L by using the first equation L = 2W + 3. This process allows us to determine the rectangle's dimensions.