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Chapter 10 Class 9 Herons Formula

Serial order wise

Last updated at May 29, 2023 by Teachoo

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 = β(s(sβa)(sβb)(s βc)) 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 = β(π (π βπ)(π βπ)(π βπ)) Putting a = 60 m , b = 100 m, c = 140 m & s = 150 m Area = β(150(150β60)(150β100)(150β140)) m2 = β(150Γ90Γ50Γ10) m2 = β( (15Γ9Γ5)Γ(10)4) = β(15Γ(3Γ3)Γ5Γ(10)4) = β(15Γ(3Γ5)Γ3Γ(10)4) = β(15Γ15Γ3Γ(10)4) = β((15)2Γ3Γ(10)4) = β((15)2)Γβ3Γ β104 = (15) Γβ3Γ γ(104)γ^(1/2) = (15)Γβ3 Γ (102) = (15)Γβ3 Γ (100) = 1500β3 Thus, Area = 1500β3 m2