The problem in the image states:

"The length of a rectangle is 5 inches longer than its width. If the perimeter of the rectangle is 182 inches, find the length and width of the rectangle."

Let's define the variables:

• Let the width of the rectangle be $w$ inches.
• Since the length is 5 inches longer than the width, the length will be $w + 5$ inches.

The formula for the perimeter of a rectangle is given by: $P = 2(\text{Length} + \text{Width})$ Substitute the values into the formula: $182 = 2((w + 5) + w)$ Simplify the equation: $182 = 2(2w + 5)$ $182 = 4w + 10$ Subtract 10 from both sides: $172 = 4w$ Now, divide both sides by 4: $w = 43$

Now that we know the width, we can find the length: $\text{Length} = w + 5 = 43 + 5 = 48$

So, the width of the rectangle is 43 inches, and the length is 48 inches.

Would you like more details or have any further questions?

Here are some related questions to explore:

1. What is the area of the rectangle with the given dimensions?
2. How would the problem change if the perimeter were increased by 10 inches?
3. If the length were 10 inches longer than the width, how would the dimensions change?
4. Can you derive a general formula to solve such problems for any length and width relationship?
5. What would the width be if the perimeter was 200 inches instead?

Tip: Always use the correct formula for the perimeter or area depending on the given information to avoid confusion.