Math Problem Statement

The length and breadth of a rectangular field are 120 m and 75 m respectively. Find (i) the area of the field, (ii) the perimeter of the field and the cost of fencing it at ₹40 per meter.

Solution

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Example 1: Area, Perimeter, and Cost of Fencing of a Rectangular Field

  • Length of the field = 120 m, Breadth = 75 m.
  • (i) Area of the field: 120×75=9000m2120 \times 75 = 9000 \, m^2
  • (ii) Perimeter of the field: 2(120+75)=390m2(120 + 75) = 390 \, m
  • Cost of fencing: 390×40=15600Rupees390 \times 40 = 15600 \, \text{Rupees}

Example 2: Length and Breadth of a Rectangular Field with a Given Area

  • The field's area = 3456 m², and the ratio of length to breadth is 3:2.
  • Using the formula for area, we deduce the length and breadth, and the cost of fencing.

Example 3: Area of a Rectangular Plot with a Diagonal

  • One side = 35 m, diagonal = 37 m. Using the Pythagorean theorem to find the other side (BC).

Example 4: Area of a Square with a Given Diagonal

  • Diagonal of square = 8√2 m.
  • Using the formula for the area of a square (12×(diagonal)2\frac{1}{2} \times (diagonal)^2).

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Math Problem Analysis

Mathematical Concepts

Area of a Rectangle
Perimeter of a Rectangle
Cost Calculation

Formulas

Area of rectangle = Length × Breadth
Perimeter of rectangle = 2 × (Length + Breadth)
Cost of fencing = Perimeter × Cost per meter

Theorems

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Suitable Grade Level

Grades 6-8