Question

Show that if the lengths of sides of a right angled triangle are in A.P., then their
ratio is 3:4:5​

Answer 1

We have the sides of the triangle in arithmetic progression,

a−d,a,a+d

To prove it we will need the following equations,

(a−d)2+(a)2=(a+d)2

a2−2ad+d2+a2=a2+2ad+d2⟺a=4d

Its sides ratio will then become,

a−d:a:a+d

a=4d

4d−d:4d:4d+d⟺3d:4d:5d

3d:4d:5d⟺3:4:5

Tools used:

a2+b2=c2