To set up the quadratic equation, let's define the dimensions of the rectangular garden based on the information given:

1. Let the width of the garden be $w$ feet.
2. The length of the garden is 4 feet longer than the width, so the length is $w + 4$ feet.
3. The area of a rectangle is given by the formula: $\text{Area} = \text{length} \times \text{width}$

Since the area is provided as 60 square feet, we can set up the equation:

$w \times (w + 4) = 60$

Expanding this, we get:

$w^2 + 4w = 60$

Now, rearrange it to form a standard quadratic equation:

$w^2 + 4w - 60 = 0$

This is the quadratic equation that represents the problem scenario. You can now solve for $w$ to find the width, and subsequently determine the length.

Would you like assistance solving this equation?

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Related Questions

1. What is the quadratic formula used to solve equations like this?
2. How can we check the dimensions after solving to ensure the area is accurate?
3. What are possible values for the width and length that satisfy this equation?
4. Could we use factoring to solve this equation instead of the quadratic formula?
5. How does this approach apply to finding dimensions in real-world area problems?

Tip

Always start by defining variables based on the problem's information to set up the correct equation before solving.