an example of a squared frame painting that is 30cm by 30cm is shown. lucy uses 2m of timber of width 5cm to complete the picture frame what is the side length og the frame

To find the side length of the picture frame, we need to consider both the dimensions of the painting and the width of the timber used for the frame.

Given:
- The painting itself is 30 cm by 30 cm.
- The timber used for the frame has a width of 5 cm.
- Lucy has 2 meters (200 cm) of timber.

The frame is added to all four sides of the painting. Since the timber has a width of 5 cm, it will increase the dimensions of the painting by twice the width of the timber on each side.

### Step-by-Step Calculation:

1. **Increase in dimensions due to the frame:**
   - On each side of the painting, the frame adds 5 cm on the left and 5 cm on the right, and similarly on the top and bottom.
   - Therefore, the total increase in each dimension (length and width) is \(5 \, \text{cm} + 5 \, \text{cm} = 10 \, \text{cm}\).

2. **Total side length of the frame:**
   - The side length of the framed painting is \(30 \, \text{cm} + 10 \, \text{cm} = 40 \, \text{cm}\).

3. **Perimeter of the framed painting:**
   - The perimeter is \(4 \times \text{side length} = 4 \times 40 \, \text{cm} = 160 \, \text{cm}\).

Since Lucy has 2 meters (200 cm) of timber, and the total perimeter required is 160 cm, the timber she has is sufficient to frame the painting.

### Conclusion:
The side length of the frame is **40 cm**.

Would you like any additional details or have any further questions?

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Here are 5 related questions you might consider:

1. How would the side length change if the timber width was 10 cm instead of 5 cm?
2. How would you calculate the area of the framed painting?
3. If Lucy had only 1.5 meters of timber, what would be the maximum side length she could frame?
4. What would happen to the frame dimensions if the painting was rectangular instead of square?
5. How could Lucy minimize the amount of timber needed while still framing the entire painting?

**Tip:** Always double-check the units you're working with, especially when dealing with different units like meters and centimeters!

An example of a squared frame painting that is 30cm by 30cm is shown. Lucy uses 2m of timber of width 5cm to complete the picture frame. What is the side length of the frame?

Learn how to determine the side length of a framed painting using 2m of timber. This problem involves calculating the perimeter of a square frame and adjusting for the width of the timber. Suitable for students in Grades 6-8, covering geometry and measurement concepts.

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