Farmer Chilko wanted to fence a rectangular vegetable plot.

The plot was 70 metres longer than its width and will take 340 metres of fencing material.

What is the length and width of the plot?

Let's solve this problem step by step.

### Step 1: Define the variables
- Let the width of the rectangular plot be \( w \) meters.
- The length of the plot is 70 meters longer than its width, so the length can be written as \( l = w + 70 \) meters.

### Step 2: Use the perimeter formula
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2l + 2w
\]
We know that the perimeter is 340 meters. So,
\[
2l + 2w = 340
\]

### Step 3: Substitute the length
Substitute \( l = w + 70 \) into the perimeter equation:
\[
2(w + 70) + 2w = 340
\]

### Step 4: Simplify the equation
Expand and simplify the equation:
\[
2w + 140 + 2w = 340
\]
\[
4w + 140 = 340
\]

### Step 5: Solve for \( w \)
Subtract 140 from both sides:
\[
4w = 200
\]
Divide by 4:
\[
w = 50
\]

### Step 6: Find the length \( l \)
Now that we have \( w = 50 \) meters, we can find the length:
\[
l = w + 70 = 50 + 70 = 120 \text{ meters}
\]

### Final Answer:
- **Width of the plot**: 50 meters
- **Length of the plot**: 120 meters

Would you like more details on this solution, or do you have any other questions?

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**Related Questions:**

1. What would be the perimeter if the plot were 10 meters longer in both length and width?
2. How much fencing material would be needed if the width was increased by 20 meters?
3. What would the area of the plot be?
4. If the plot was a square with the same perimeter, what would be the side length?
5. How much area would be lost if the length was reduced by 10 meters?

**Tip:** Always double-check your calculations when working with perimeter and area to ensure accuracy.

Learn how to calculate the length and width of a rectangular vegetable plot given its perimeter and the relationship between its length and width. Follow a step-by-step solution to find the dimensions of the plot, which is 70 meters longer than its width and requires 340 meters of fencing material. Suitable for students in Grades 6-8.

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