Question

Q. Sides of a triangle are in AP then the ratio of length of sides will be?
A. 2:3:4

I need explanation

Answer 1

Answer:

Let a−d,a,a+d be the sides of Right angled triangles, which are in AP with first term a and common difference d.

∴(a+d)

2

=a

2

+(a−d)

2

(∵ of right angled triangle.)

⇒a

2

+2ad+d

2

=a

2

+a

2

−2ad+d

2

⇒a

2

−4ad=0

⇒a(a−4d)=0

⇒a=0,4d

But, a=0 is not possible.

Therefore, a=4d.

Hence side are 3d,4d,5d.

i.e they are in ratio 3:4:5

Option C is correct.