If the sides of a right-triangle are in A.P., then the sides are in what proportion?
Explanation:
Let the sides of the triangle be a –d, a, a + d, then hypotenuse being the greatest side i.e. a + d.
So (a + d)2 = a2 + (a – d)2
⇒ a2 + d2 + 2ad = 2a2 - 2ad + d2
⇒ a = 4d.
Therefore ratio of the sides = a – d : a : a + d = (4d – d) : 4d : (4d + d) = 3 : 4 : 5.
Hence, option (a).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.