A square garden has a walkway 5 feet wide around its corner edge. If the area of the entire garden, including the walkways is 10,000 square feet, then what are the dimensions of the planted area?

Let the side length of the planted area (the square garden without the walkway) be denoted by \( x \) feet. The walkway is 5 feet wide on all sides, so the total side length of the entire garden (including the walkway) will be \( x + 2(5) = x + 10 \) feet.

The area of the entire garden, including the walkway, is given as 10,000 square feet. The area of a square is the square of its side length, so the equation for the total area is:

\[
(x + 10)^2 = 10,000
\]

Taking the square root of both sides:

\[
x + 10 = \sqrt{10,000} = 100
\]

Now, solving for \( x \):

\[
x = 100 - 10 = 90 \, \text{feet}
\]

Thus, the side length of the planted area is \( \boxed{90} \) feet.

### Do you want more details or have any questions?

Here are 5 related questions you could explore:
1. What is the total length of the walkway?
2. How much area is occupied by the walkway alone?
3. If the walkway width was changed, how would the dimensions of the planted area change?
4. How much fencing would be needed to surround the entire garden, including the walkway?
5. What would happen to the planted area if the garden's total area was increased to 12,000 square feet?

**Tip:** When dealing with geometric problems, drawing a diagram can help clarify the relationships between different parts of the figure.

A square garden has a walkway 5 feet wide around its corner edge. If the area of the entire garden, including the walkways, is 10,000 square feet, then what are the dimensions of the planted area?

Learn how to find the dimensions of the planted area in a square garden that includes a 5-foot-wide walkway around its edge. The total area of the garden is 10,000 square feet. This problem covers key algebra and geometry concepts, suitable for Grades 8-10.

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