Let's solve the problem step-by-step.

Step-by-Step Solution:

1. Initial Rectangle Perimeter:

   • The perimeter of the original rectangle is given as 24 inches.
   • Let the length of the rectangle be $l$ and the width be $w$.
   • The perimeter formula is: $2l + 2w = 24$
   • Simplifying, we get: $l + w = 12 \quad \text{(Equation 1)}$

2. Understanding the Change after Cutting Squares:

   • Small squares with a side of 1 inch are cut out from each corner of the rectangle.
   • This reduces the length by 2 inches (1 inch from each end) and the width by 2 inches.

3. Dimensions of the New Figure:

   • New length = $l' = l - 2$
   • New width = $w' = w - 2$

4. New Perimeter Calculation:

   • The perimeter of the new figure (which is also a rectangle) is given by: $\text{New Perimeter} = 2l' + 2w'$
   • Substituting $l'$ and $w'$: $\text{New Perimeter} = 2(l - 2) + 2(w - 2)$ $\text{New Perimeter} = 2l + 2w - 4 - 4$ $\text{New Perimeter} = 2l + 2w - 8$
   • From Equation 1, $2l + 2w = 24$: $\text{New Perimeter} = 24 - 8 = 16 \text{ inches}$

Conclusion:

The perimeter of the resulting figure after cutting out the 1-inch squares from each corner is 16 inches.

Would you like to explore more details or ask any further questions?

Here are 5 related questions to consider:

1. How would the perimeter change if larger squares were cut out?
2. How can you determine the area of the new figure after cutting the squares?
3. If the original area of the rectangle was known, how would the area of the resulting figure be calculated?
4. How does cutting squares from the corners affect the overall shape and dimensions of the rectangle?
5. What would be the new perimeter if the cuts were made at different dimensions, say 2 inches?

Tip: When modifying the dimensions of a shape by cutting or adding, always account for how these changes affect both the length and width simultaneously.