Math Problem Statement

A rectangular field has its length 2 meters greater than its breadth, and its perimeter is 68 meters. Find the dimensions of the field. Additionally, if the cost of fencing is 20 taka per meter, calculate the total cost.

Solution

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Problem Breakdown:

  1. A rectangular field has its length 2 meters greater than its breadth, and its perimeter is 68 meters.
    • a) Determine the dimensions (length and breadth) of the field.
    • b) If the cost of fencing the field is 20 taka per meter, calculate the total fencing cost.

Solution:

Part (a): Dimensions of the Field

  1. Let the breadth of the field be x meters.

    • Then, the length will be (x + 2) meters.
  2. The formula for the perimeter of a rectangle is: Perimeter=2×(Length+Breadth)\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth}) Substituting the given perimeter (68 meters): 68=2×(x+(x+2))68 = 2 \times \left( x + (x + 2) \right)

  3. Simplify the equation: 68=2×(2x+2)68 = 2 \times (2x + 2) 68=4x+468 = 4x + 4

  4. Solve for x: 4x=6844x = 68 - 4 4x=644x = 64 x=16x = 16

  5. So, the breadth is 16 meters, and the length is: x+2=16+2=18 meters.x + 2 = 16 + 2 = 18 \text{ meters}.

Part (b): Cost of Fencing

  1. Total length of the fence is the perimeter, which is 68 meters.
  2. Cost of fencing per meter = 20 taka.
  3. Total cost of fencing: Total cost=Perimeter×Cost per meter\text{Total cost} = \text{Perimeter} \times \text{Cost per meter} Total cost=68×20=1360 taka.\text{Total cost} = 68 \times 20 = 1360 \text{ taka}.

Final

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Perimeter Calculation

Formulas

Perimeter of a rectangle = 2 × (Length + Breadth)
Cost = Perimeter × Rate per meter

Theorems

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Suitable Grade Level

Grades 6-8