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if the sides of a triangle are in AP and the greatest angle of the triangle is double the smallest angle the ratio of the sides of the triangle is

if the sides of a triangle are in AP and the greatest angle of the triangle is double the smallest angle the ratio of the sides of the triangle is
 

Grade:12

1 Answers

Rahul Rawat
34 Points
7 years ago
Let the side of triangles a, b, c. Also, the side in AP so , a + c = 2b. ---------------1And also by angle relationship We can easily proof that c² = a(a+c) ------------2 from eq 1 and 2 c² = a(2b) c² = 2ab c = √2ab Now ratio becomes a : b : c = a : b : √2ab Dividing by √ab. √a/√b : √b/√a : √2Or √(a/b) : √(b/a) : √2. Now, from eq 2 a + √(2ab) = 2b adding 2b/4 on both side Then after solving we can get √a = (√5b -√b)/√2Therefore √(a/b) = (√5 - 1) /√2 √(b/a) = (√5 +1 )/ 2√2 The side of triangle in the ratio of 2√5 - 2 : √5 + 1 : 4

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