The perimeter of a rectangle is 46 metres.  The length is one metre less than twice the width.  What is the length of the rectangle?    Include "let statements" for your variables as we did in class.

Given the problem, let's define the variables using "let statements" and solve for the length of the rectangle.

### Step 1: Set up the variables

1. **Let** the width of the rectangle be \( w \) metres.
2. **Let** the length of the rectangle be \( l \) metres.

### Step 2: Define relationships between the variables

1. According to the problem, the length is one metre less than twice the width. This can be written as:
   \[
   l = 2w - 1
   \]

2. The formula for the perimeter of a rectangle is:
   \[
   \text{Perimeter} = 2l + 2w
   \]
   Given that the perimeter is 46 metres, we can set up the equation:
   \[
   2l + 2w = 46
   \]

### Step 3: Substitute the relationship into the equation

Since \( l = 2w - 1 \), substitute this into the perimeter equation:
\[
2(2w - 1) + 2w = 46
\]

### Step 4: Simplify and solve for \( w \)

1. Distribute the 2 into the parentheses:
   \[
   4w - 2 + 2w = 46
   \]

2. Combine like terms:
   \[
   6w - 2 = 46
   \]

3. Add 2 to both sides:
   \[
   6w = 48
   \]

4. Divide by 6:
   \[
   w = 8
   \]

### Step 5: Find the length

Since \( l = 2w - 1 \):
\[
l = 2(8) - 1 = 16 - 1 = 15
\]

### Final Answer

The length of the rectangle is **15 metres**.

Would you like more details or have any questions?

### Relative Questions

1. What would the length be if the perimeter was 60 metres instead?
2. If the width of the rectangle was increased by 3 metres, what would be the new perimeter?
3. How would the relationship change if the length was 3 metres less than twice the width?
4. Can you express the width in terms of the perimeter and length?
5. If the rectangle's area needs to be 120 square metres, how would you find the new dimensions?

### Tip

Always clearly define your variables with "let statements" before starting to solve equations. This helps in understanding the problem better and keeping track of your calculations.

The perimeter of a rectangle is 46 metres. The length is one metre less than twice the width. What is the length of the rectangle? Include 'let statements' for your variables as we did in class.

Learn how to find the length of a rectangle with a perimeter of 46 metres and a length that is one metre less than twice the width. This problem explores key concepts in algebra and geometry, including linear equations and the properties of rectangles. Suitable for students in Grades 6-8.

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