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Example 3 - The sides of a triangular plot are in ratio - Examples

Example 3 - Chapter 12 Class 9 Herons Formula - Part 2
Example 3 - Chapter 12 Class 9 Herons Formula - Part 3 Example 3 - Chapter 12 Class 9 Herons Formula - Part 4


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Example 3 The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area. 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 Given Perimeter = 300 m Semi-Perimeter = s =Perimeter/2 s = 300/2 s = 150 m Given Ratio of sides is 3 : 5 : 7 Let sides be a = 3x meters , b = 5x meters , c = 7x meters where x is any number Now, Perimeter = 300 m a + b + c = 300 3x + 5x + 7x = 300 15x = 300 x = 300/15 x = 20 So, a = 3x meter b = 5x m c = 7x m Area of triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a = 60 m , b = 100 m, c = 140 m & s = 150 m Area = √(150(150−60)(150−100)(150−140)) m2 = √(150×90×50×10) m2 = √( (15×9×5)×(10)4) = √(15×(3×3)×5×(10)4) = √(15×(3×5)×3×(10)4) = √(15×15×3×(10)4) = √((15)2×3×(10)4) = √((15)2)×√3× √104 = (15) ×√3× 〖(104)〗^(1/2) = (15)×√3 × (102) = (15)×√3 × (100) = 1500√3 Thus, Area = 1500√3 m2

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.