The sides of a right triangle are in arithmetic progression.Let one of the legs be x, the other leg x+d, and the hypotenuse x+2d.

Then by the Pythagorean theorem we have:

`x^2+(x+d)^2=(x+2d)^2`

`x^2+x^2+2dx+d^2=x^2+4dx+4d^2`

`3d^2+2dx-x^2=0`

`(3d-x)(d+x)=0`

`==>3d=x` or `d=-x`

We want the ratio of the legs or `x/(x+d)`

If `d=-x` this makes no sense in the problem as one of the sides has length 0.

`3d=x==>x/(x+d)=(3d)/(3d+d)=3/4`

So the ratio of sides is 3:4.

**The answer is (c) `3/5,4/5` **

**Note that this is a Pythagorean triple: `3/5,4/5,5/5` with common difference `1/5`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now