Math Problem Statement

A rectangular field's dimensions are changed as follows: its length increases by 2 meters, and its breadth increases by 6 meters, resulting in an area of 84 square meters. Calculate the perimeter of the field. Additionally, if fencing costs 20 Taka for every 25 meters, determine the total fencing cost.

Solution

To solve the problem in the uploaded image, let's break it down into parts based on the Bengali text.

Question Breakdown:

  1. The rectangular field has:

    • Length increased by 2 meters.
    • Breadth increased by 6 meters.
    • The total area becomes 84 square meters.

    Find the perimeter of the field.

  2. Every 25 meters of boundary fence costs 20 Taka. Calculate the total cost of fencing the entire boundary.


Solution:

Part 1: Finding Dimensions and Perimeter

  1. Let the original length be ll meters and breadth be bb meters.

  2. From the given changes:

    • New length = l+2l + 2
    • New breadth = b+6b + 6
  3. Area of the rectangle: (l+2)(b+6)=84(l + 2)(b + 6) = 84 Expanding: lb+6l+2b+12=84lb+6l+2b=72(Equation 1)lb + 6l + 2b + 12 = 84 \quad \Rightarrow \quad lb + 6l + 2b = 72 \quad \text{(Equation 1)}

    Since

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Math Problem Analysis

Mathematical Concepts

Algebra
Area and Perimeter
Proportions

Formulas

Area of rectangle: Area = length × breadth
Perimeter of rectangle: Perimeter = 2 × (length + breadth)

Theorems

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Suitable Grade Level

Grades 7-9