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if the angles of a right angled triangle are in A.P, then ratio of its sides
Let the sides of the right triangle be, a - d , a and a+ dnow, (a + d)2 = (a - d)2 + a2 [Pythagoras theorem] so, a2 + d2 + 2ad = a2 + d2 - 2ad + a2 ⇒ 4ad = a2 ⇒ a = 4dso 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
Let the sides of the right triangle be, a - d , a and a+ d
now, (a + d)2 = (a - d)2 + a2 [Pythagoras theorem]
so, a2 + d2 + 2ad = a2 + d2 - 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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