the sides of a right angle triangle are aada2d

Question

the sides of a right angle triangle are a,a+d,a+2d with a and d both positive.the ratio of a to d 

a)1:2 b)1:3 c)3:1 d)5:2

answer is (c) i.e. 3:1

Solution: Applying Pythagoras Theorem,

we get, (a+2d)²=a²+(a+d)²

=> a²+4d²+4ad=a²+a²+d²+2ad

=> 3d²+2ad-a²=0

=> (d+a)(3d-a)=0

neglecting (d+a)=0, by solving for (3d-a)=0, we get a:d=3:1