Problem solving is a fundamental skill that involves systematic approaches to finding solutions. The problem-solving cycle consists of four key steps: first, understand the problem by identifying what is given and what needs to be found; second, plan your approach by choosing appropriate strategies; third, execute your plan step by step; and finally, review your solution to ensure it makes sense.
Understanding the problem is crucial for successful problem solving. We need to carefully read the problem statement and identify three key components: what information is given, what we need to find, and any constraints or relationships. In this rectangle problem, we're given that the perimeter is 24 centimeters and the length is twice the width. We need to find both the length and width dimensions.
Planning the solution is the second crucial step in problem solving. We start by defining our variables: let w represent the width, and since the length is twice the width, l equals 2w. Next, we use the perimeter formula: perimeter equals 2 times length plus 2 times width, which equals 24. Substituting our relationship, we get 2 times 2w plus 2w equals 24, which simplifies to 6w equals 24, giving us w equals 4 centimeters.
Now we execute our plan to find the complete solution. Since w equals 4 centimeters, and the length is twice the width, l equals 2 times 4, which is 8 centimeters. To verify our answer, we check the perimeter: 2 times 8 plus 2 times 4 equals 16 plus 8, which equals 24 centimeters. This matches our given perimeter, confirming our solution is correct.
To become an effective problem solver, follow these key tips: First, read the problem carefully multiple times to ensure full understanding. Second, draw diagrams or visual representations when possible, as they often reveal important relationships. Third, consider working backwards from what you need to find. Fourth, always check your units and verify that your answer is reasonable. Finally, practice similar problems regularly to build your skills. Remember to avoid common mistakes like rushing without understanding, skipping verification, or not clearly defining your variables.