To solve this problem, we need to set up an equation using the given information and then solve for the width and length of the rectangular garden.
Given information:
- The length of the rectangular garden is 5 feet less than 3 times its width.
- The area of the rectangular garden is 303 square feet.
Let's define the variables:
- Let the width of the rectangular garden be w feet.
- Then, the length of the rectangular garden is 3w - 5 feet.
Step 1: Set up the equation for the area of the rectangular garden.
Area = Length × Width
303 = (3w - 5) × w
303 = 3w^2 - 5w
Step 2: Solve the quadratic equation for the width (w).
3w^2 - 5w - 303 = 0
Solving the equation using the quadratic formula:
w = (5 ± √(5^2 - 4 × 3 × -303)) / (2 × 3)
w = (5 ± √(25 + 3636)) / 6
w = (5 ± √3661) / 6
w = (5 ± 60.5) / 6
There are two possible solutions for the width:
w = (5 + 60.5) / 6 = 10.75 feet
w = (5 - 60.5) / 6 = -9.25 feet (this solution is not valid as the width cannot be negative)
Therefore, the width of the rectangular garden is 10.75 feet.
Step 3: Calculate the length of the rectangular garden.
Length = 3w - 5
Length = 3 × 10.75 - 5 = 27.25 feet
Therefore, the width of the rectangular garden is 10.75 feet, and the length of the rectangular garden is 27.25 feet.
