Final answer:
To find the width and length of the garden described in the question, set up and solve a quadratic equation based on the information that the length is 5 feet less than 3 times the width and that the area is 307 square feet. Solve for the width first, then calculate the length.
Step-by-step explanation:
The student is trying to find the dimensions (length and width) of a rectangular garden given that the length is 5 feet less than 3 times its width and that the area of the garden is 307 square feet. To solve for the width and length, we can set up a system of equations based on the given information:
- Let w represent the width of the garden.
- Then the length l would be 3w - 5 (5 feet less than 3 times the width).
- The area of a rectangle is calculated as length × width, which in this case is l × w = 307.
Now we plug in the expression for l (3w - 5) into the area equation:
- w × (3w - 5) = 307
- 3w^2 - 5w - 307 = 0
Solving this quadratic equation for w, we find the width of the garden. After finding w, we can calculate l by substituting the value of w into l = 3w - 5.