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.