Math Problem Statement

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

Solution

To find the dimensions of the planted area of the square garden, we can proceed step-by-step:

Step 1: Define variables

Let xx be the side length of the planted square garden (without the walkway). The walkway is 5 feet wide all around, so the total side length of the garden including the walkway will be x+2(5)=x+10x + 2(5) = x + 10 feet.

Step 2: Total area (including walkway)

The total area of the garden, including the walkway, is given as 10,000 square feet. So, the equation for the total area is: (x+10)2=10,000(x + 10)^2 = 10,000

Step 3: Solve for xx

Now solve for xx: x+10=10,000=100x + 10 = \sqrt{10,000} = 100 x=10010=90x = 100 - 10 = 90

Step 4: Conclusion

The side length of the planted area is 90 feet. Since it's a square garden, the dimensions of the planted area are: 90 feet×90 feet\boxed{90 \text{ feet} \times 90 \text{ feet}}

Would you like more details or have any further questions?

Here are some related questions to explore:

  1. What is the perimeter of the planted area?
  2. How much area is covered by the walkway alone?
  3. What would the dimensions be if the walkway was 10 feet wide instead?
  4. How would the dimensions change if the total area was reduced to 8,000 square feet?
  5. How would you solve this problem if the garden was a rectangle instead of a square?

Tip: When solving geometry problems with additional structures like walkways, always start by defining the variables for the core area and then account for the added dimensions systematically.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of a Square
Algebra

Formulas

Area of a square: A = s^2
Solving equations involving square roots

Theorems

Pythagorean Theorem (implicitly related in walkway dimension context)

Suitable Grade Level

Grades 8-10