A park has a square flower bed with a path around it. The path is 5 meters wide, and the total area of the park is 121 square meters. What are the dimensions of the flower bed

Let the side length of the square flower bed be \( x \) meters.

Since the path is 5 meters wide around the flower bed, the total side length of the park (including the flower bed and the path) is \( x + 2(5) = x + 10 \) meters.

The total area of the park is given as 121 square meters, so:
\[
(x + 10)^2 = 121
\]
Taking the square root of both sides:
\[
x + 10 = 11
\]
Solving for \( x \):
\[
x = 11 - 10 = 1
\]

Thus, the side length of the square flower bed is **1 meter**.

### Would you like more details or have any questions?

Here are some related questions:
1. What is the area of the flower bed itself?
2. How can the width of the path affect the overall park area?
3. If the path width increased by 1 meter, what would the new park area be?
4. How would you calculate the total perimeter of the park including the path?
5. What if the park were rectangular, how would the problem change?

**Tip:** Always check whether you're dealing with the total dimensions of an area or just a part of it when solving geometry problems.

A park has a square flower bed with a path around it. The path is 5 meters wide, and the total area of the park is 121 square meters. What are the dimensions of the flower bed?

Learn how to calculate the dimensions of a square flower bed when given the total area of a park and the width of the surrounding path. This problem involves key algebraic and geometric concepts, such as the area of squares and solving basic equations. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation