The problem involves the perimeter and cost calculation for a rectangular field based on the given conditions. Let me solve it step-by-step:

Problem:

1. The length of the rectangular field is 2 meters more than its width.
2. The perimeter of the field is 64 meters.

Tasks:

• (a) Determine the dimensions of the field (length and width).
• (b) If the cost of fencing per meter is 25 BDT, calculate the total cost.

Solution:

Part (a): Dimensions of the field

1. Let the width of the field be $x$ meters.
   Then, the length of the field will be $x + 2$ meters.

2. The formula for the perimeter of a rectangle is: $\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$

3. Substituting the values: $64 = 2 \times \left( (x + 2) + x \right)$ Simplifying: $64 = 2 \times (2x + 2)$ $64 = 4x + 4$ $4x = 60 \quad \Rightarrow \quad x = 15$

4. Therefore:

   • Width = $x = 15$ meters
   • Length = $x + 2 = 15 + 2 = 17$ meters

Part (b): Cost of fencing

1. Total perimeter = 64 meters
   Cost of fencing per meter = 25 BDT.

2. Total cost: $\text{Total cost} = 64 \times 25 = 1600 \, \text{BDT}.$

Final Answer:

1. Dimensions of the field:
   • Width = 15 meters
   • Length = 17 meters
2. Total fencing cost = 1600 BDT.

Would you like a detailed explanation of any step or have additional questions?

Related Questions:

1. How do you derive the perimeter formula for a rectangle?
2. What happens if the length is given instead of the width?
3. How can you calculate the area of this field?
4. What is the cost if the price per meter is increased to 30 BDT?
5. How does changing the length-to-width ratio affect the perimeter?

Tip:

Always check your equation setup against the problem statement to avoid missing constraints.