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if the angles of a right angled triangle are in A.P, then ratio of its sides

if the angles of a right angled triangle are in A.P, then ratio of its sides

Grade:12

1 Answers

Arun
25763 Points
3 years ago

Let the sides of the right triangle be, a - d , a and a+ d

now, (a + d)= (a - d)+ a2  [Pythagoras theorem]

 so, a+ d+ 2ad = a+ d- 2ad + a2

 ⇒ 4ad = a2

 ⇒ a = 4d

so the sides of triangle are : 3d, 4d and 5d  [on substituting the value of a]

Hence the sides of the right triangle are in the ratio  of 3 : 4 : 5 

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