Q. If the sides of sides of a right angled triangle are in AP, then the sides are proportional to
A) 1 : 2 : 3
B) 2 : 3 : 4
C) 3 : 4 : 5
D) 4 : 5 : 6
Explanation
(c)
Let the sides of the right triangle be $a - d,\ a,a + d\$, then hypotenuse being the greatest side $ie,\ a + d.$
So, $(a + d)^{2} = a^{2} + (a - d)^{2}$
$\Rightarrow \ \ a^{2} + d^{2} + 2ad = a^{2} - 2ad + d^{2}$
$\Rightarrow \ \ a = 4d$
Therefore, ratio in the sides $= a - d\ :a\ :a + d = (4d - d):4d:(4d + d) = 3\ :4\ :5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.