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

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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(sβˆ’a)(sβˆ’b)(s βˆ’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 βˆ’π‘Ž)(𝑠 βˆ’π‘)(𝑠 βˆ’π‘)) Putting a = 60 m , b = 100 m, c = 140 m & s = 150 m Area = √(150(150βˆ’60)(150βˆ’100)(150βˆ’140)) m2 = √(150Γ—90Γ—50Γ—10) m2 = √( (15Γ—9Γ—5)Γ—(10)4) = √(15Γ—(3Γ—3)Γ—5Γ—(10)4) = √(15Γ—(3Γ—5)Γ—3Γ—(10)4) = √(15Γ—15Γ—3Γ—(10)4) = √((15)2Γ—3Γ—(10)4) = √((15)2)Γ—βˆš3Γ— √104 = (15) Γ—βˆš3Γ— γ€–(104)γ€—^(1/2) = (15)Γ—βˆš3 Γ— (102) = (15)Γ—βˆš3 Γ— (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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.