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Ex 12.1, 5 - Sides of a triangle are in ratio 12: 17: 25 - Finding area of triangle

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
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Ex 12.1, 5 Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. 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 = 540 cm Semi-Perimeter = s = Perimeter/2 s = 540/2 s = 270 cm Given Ratio of sides is 12 : 17 : 25 Let sides be a = 12x cm ,b = 17x cm , c = 25x cm where x is any number Now, Perimeter = 540 cm a + b + c = 540 12x + 17x + 25x = 540 29x + 25x = 540 54x = 540 x = 540/54 x = 10 So, a = 12x cm b = 17x cm c = 25x cm Area of triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a =120 cm, b = 170 cm, c = 250 cm & s = 270 cm Area = √(270(270−120)(270−170)(270−250)) cm2 = √(270×150×100×20) m2 = √( (27×15×2)×(10)5) = √( (27×30)×(10)5) = √( (27×3)×(10)6) = √( (81)×(10)6) = √81 × √((10)6) = √92 × √((10)6) = (9) × 〖(106)〗^(1/2) = (9)× (103) = 9000 Thus, Area = 9000 cm2

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