Certainly! Let's break down the problem step by step:

The given data is:

• The perimeter of a 5-sided figure is 45.56 meters.
• Two of the sides have the same length (let's call each of these sides x).
• The sum of the other three side lengths is 24.2 meters.

Step-by-step approach:

1. Total perimeter equation: Since the perimeter is the total sum of all five side lengths, we can write the equation as: $\text{Perimeter} = \text{Sum of all sides} = x + x + 24.2$ This simplifies to: $45.56 = 2x + 24.2$

2. Solve for $x$: We can solve for $x$ by isolating it: $45.56 - 24.2 = 2x$ $21.36 = 2x$ Now divide by 2: $x = \frac{21.36}{2} = 10.68$

Thus, each of the two sides that have the same length is 10.68 meters long.

Explanation:

• The total perimeter is the sum of all five sides.
• Since we know the sum of the three other sides, we can subtract that from the total perimeter to find the combined length of the two equal sides.
• Finally, we divide the remaining value by 2 to find the length of each of the two equal sides.

Would you like further details on this, or do you have any questions?

Related Questions:

1. How would this change if the perimeter was different, but the same conditions applied?
2. What if the figure had 6 sides, with three sides of the same length?
3. Can you find the length of the remaining sides if only the total perimeter and one side length are given?
4. How would you handle this if one of the sides was a variable fraction of another?
5. How could you use algebraic expressions to represent a shape with an unknown number of sides?

Tip:

When solving for unknowns in word problems, always try to represent all the given information as equations. This helps break the problem into manageable steps.