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Let's go over the problem and the solutions given:

1. **Problem (d)** states that a rectangular field has:
   - Length: \( x \) meters.
   - Width: \( 2x - 5 \) meters.

(i) We are asked to show that the perimeter of the field is \( 6x - 10 \) meters.

To calculate the perimeter \( P \) of a rectangle, we use the formula:
\[
P = 2(\text{Length} + \text{Width})
\]
Substituting the given values of length \( x \) and width \( 2x - 5 \), we get:
\[
P = 2(x + (2x - 5)) = 2(3x - 5) = 6x - 10
\]
So, the solution provided is correct. This shows that the perimeter of the field is indeed \( 6x - 10 \) meters.

(ii) In this part, the perimeter is given as 50 meters, and we are asked to find the length of the field.

Using the equation for the perimeter:
\[
6x - 10 = 50
\]
Now, solve for \( x \):
\[
6x = 50 + 10 = 60
\]
\[
x = \frac{60}{6} = 10
\]
Thus, the length of the field is \( x = 10 \) meters.

---

Would you like more details on any specific part of the solution? Here are some related questions to help expand understanding:

1. What would the perimeter be if the length was doubled but the width stayed the same?
2. How would the perimeter formula change if the width was \( 3x - 2 \) instead of \( 2x - 5 \)?
3. Can you calculate the area of the field when the length is \( 10 \) meters and the width is \( 2x - 5 \)?
4. What happens to the perimeter if \( x \) is increased by 5 meters?
5. How would you find the width if the area of the field was also given?

**Tip**: Always check if the given formulas match the actual dimensions provided before solving. This ensures correctness throughout the calculations.

A rectangular field has a length of x metres. The width of the field is (2x - 5) metres. Show that the perimeter of the field is (6x - 10) metres. The perimeter of the field is 50 metres. Find the length of the field.

Solve a problem involving the perimeter of a rectangular field where the length is x meters and the width is (2x - 5) meters. Learn how to derive the perimeter formula (6x - 10) meters and find the length when the perimeter is 50 meters. Suitable for Grades 7-9.

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