The perimeter of a rectangular garden is numerically equal to thrice the area of the rectangle.  If the width of the rectangle is 1 cm, then what is the length of the rectangle?

Let's define the variables for the dimensions of the rectangle:
- Let the length of the rectangle be \( l \) cm.
- The width of the rectangle is given as \( w = 1 \) cm.

### Step 1: Write down the formulas for the perimeter and area of a rectangle

1. **Perimeter (P)** of a rectangle is given by:
   \[
   P = 2(l + w)
   \]

2. **Area (A)** of a rectangle is given by:
   \[
   A = l \times w
   \]

### Step 2: Substitute the given values

Since the width \( w = 1 \) cm, we can substitute it into the formulas:

\[
P = 2(l + 1)
\]
\[
A = l \times 1 = l
\]

### Step 3: Set up the equation based on the given condition

The perimeter is numerically equal to thrice the area:

\[
P = 3A
\]

Substitute the expressions for \( P \) and \( A \):

\[
2(l + 1) = 3l
\]

### Step 4: Solve for the length \( l \)

Expand and rearrange the equation:

\[
2l + 2 = 3l
\]

Subtract \( 2l \) from both sides:

\[
2 = l
\]

### Step 5: Conclusion

The length of the rectangle is \( \boxed{2} \) cm.

Would you like more details or have any questions? Here are five related questions to expand your understanding:

1. How would the solution change if the width was different?
2. What is the area of the rectangle with the given dimensions?
3. How would you calculate the diagonal length of the rectangle?
4. Can you derive a general formula for length in terms of width given the same condition?
5. How would the problem change if the perimeter was twice the area instead of thrice?

**Tip:** Always check if your solution makes sense by substituting back into the original conditions.

The perimeter of a rectangular garden is numerically equal to thrice the area of the rectangle. If the width of the rectangle is 1 cm, then what is the length of the rectangle?

Learn how to solve a problem where the perimeter of a rectangle is equal to three times the area, and the width is 1 cm. This step-by-step solution covers key concepts from geometry and algebra, suitable for students in Grades 6-8.

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