Reflection on Problem Solving: Wrapping Paper Puzzle

Can a rectangular piece of wrapping paper with an area of 81 square inches have a perimeter of 60?

Is it mathematically possible to have a rectangular piece of wrapping paper with these specific dimensions?

Answer:

Yes, it is mathematically possible to have a rectangular piece of wrapping paper with an area of 81 square inches and a perimeter of 60.

Problem-solving often involves logical thinking and creative approaches to finding solutions. In this particular puzzle, we are presented with a rectangular piece of wrapping paper with an area of 81 square inches and a perimeter of 60. The given hint "Let length=30-w" guides us in the right direction.

We know that the formula for the area of a rectangle is length multiplied by width, and the formula for the perimeter is 2 times the sum of length and width. By utilizing these formulas and the hint provided, we can work through the problem step by step.

Since the area of the wrapping paper is 81 square inches, and it can be divided by 9, 27, or 3, we can try substituting different values for w to find a solution that satisfies the given conditions.

If we take w as 3, then the length would be 30-3=27. This means the length is 27 and the width is 3, giving us an area of 27x3=81 square inches. With these dimensions, the perimeter of the wrapping paper would indeed be 60, meeting the conditions of the problem.

This problem highlights the importance of thinking creatively and systematically when faced with challenges. By considering the relationships between different parameters and using hints effectively, we can arrive at solutions that may initially seem impossible. It reminds us that persistence and logical reasoning are key elements in successful problem-solving.