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In this problem, you're asked if increasing the length of a figure (presumably a rectangle) by 5 inches will result in an increase in the perimeter, and by how much.

The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (\text{length} + \text{width})
\]
If the length is increased by 5 inches, the new length will be \( \text{length} + 5 \). Let's examine the change in the perimeter:

1. The original perimeter: 
   \[
   P = 2 \times (\text{length} + \text{width})
   \]
2. The new perimeter after increasing the length by 5 inches:
   \[
   P_{\text{new}} = 2 \times ((\text{length} + 5) + \text{width}) = 2 \times (\text{length} + \text{width} + 5)
   \]
   \[
   P_{\text{new}} = 2 \times (\text{length} + \text{width}) + 10
   \]

Thus, the perimeter will increase by 10 inches, which is twice the increase in the length (because the perimeter counts both the left and right sides).

Answer:
- **The perimeter will increase.**
- **The perimeter changed by 10 inches.**

Do you want further details or have any questions?

Here are 5 related questions:
1. How would the perimeter change if both the length and width increased by 5 inches?
2. How is the perimeter formula derived for different shapes, such as triangles or circles?
3. What happens to the area of the rectangle if the length is increased by 5 inches?
4. If only the width were increased by 5 inches, how would the perimeter change?
5. How does the perimeter differ for three-dimensional shapes like cubes?

**Tip:** For a rectangle, the perimeter changes by double the increase in either the length or width, since both opposite sides contribute to the total perimeter.

If the length is increased by 5 inches, will the perimeter also increase? By how much?

Learn how the perimeter of a rectangle changes when the length increases by 5 inches. This problem explores basic geometry concepts like the perimeter formula and shows how a length increase affects the perimeter. Suitable for students in Grades 5-7.

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