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Example 2 - A gardener Dhania has to put a fence all - Examples

 

  1. Class 9
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Example 2 A triangular park ABC has sides 120m, 80m and 50m. A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of Rs 20 per metre leaving a space 3m wide for a gate on one side First we find area needed to plant. Area to be planted = Area of ∆ABC Area of ∆ABC Area of triangle = √(s(s−a)(s−b)(s −c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Here, a = 50 m , b = 80 m, c = 120 m s = (𝑎 + 𝑏 + 𝑐)/2 Area of the triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a = 50 m , b = 80 m, c = 120 m & s = 125 m = √(125×(125−50)×(125−80)×(125−120)) = √(125×(75)×(45)×(5)) m2 = √((25×5)×(25×3)×(5×9)×(5)) m2 = √((25×25)×(5×5)×(9)×(3×5)) m2 = √((252)×(52)×(32)×(3×5)) m2 = √252 × √52 × √32 × √15 = 25 × 5 × 3 × √15 = 375 √15 m2 Area needed to plant = 375 √15 m2 Finding cost of fencing Number of meters to be fenced = 250 – 3 = 247 m Cost of fencing = Rs 20 per metre. Cost of fencing park = Rs 20 × 247 = Rs 4940

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