The image you uploaded contains three problems related to geometry, particularly involving the area and volume of rectangular and square shapes. Let's solve each problem step by step:

Problem 1:

The problem states that the area of the rectangular garden is $63 \, \text{m}^2$. You are asked to find the width of the path around the garden.

Let’s denote:

• $l$ as the length of the rectangular garden
• $w$ as the width of the garden
• The area formula for a rectangle is $\text{Area} = l \times w$

Since we are given that the area is $63 \, \text{m}^2$, we can write: $l \times w = 63$ We need more information to solve this exactly. Please check for any additional measurements for this problem.

Problem 2:

In this problem, you are dealing with a square flower bed that has a side length of $x$. There is a path of width 3 meters around the flower bed, and it is stated that the remaining area of the flower bed is 70 $\text{m}^2$.

Step 1: Set up the equation

• The area of the entire flower bed (including the path) would be $(x + 6)^2$, since the path adds 3 meters on both sides.
• The area of the path alone is the difference between the entire area and the flower bed area. So, the remaining area of the flower bed is $70 \, \text{m}^2$. $x^2 = 70$

Step 2: Solve for $x$

$x = \sqrt{70} \approx 8.37 \, \text{m}$

So, the side length of the original flower bed is approximately $8.37 \, \text{m}$.

Problem 3:

In this problem, a square paper with side length $x$ is cut into a square of side length 4 cm. The remaining paper is folded into a box, and the volume of the box is $256 \, \text{cm}^3$.

Step 1: Set up the equation

• The side length of the original square paper is $x$.
• The side of the smaller square that was cut off is 4 cm, leaving a box with a certain height and base area.

To solve for the exact dimensions, it is important to know more about how the box was formed (e.g., its height or whether it's a cube). If any additional information is given on the image, please let me know.

Let me know if you'd like to further discuss any of these problems or if there are any more clarifications on the image.