If the sides of a right angled triangle are in AP, then the sides of the acute angles are: The options a. sq.rt 3,1/sq.rt 3  b.sq.rt(sq.rt5-1)/2, sq.rt(sq.rt5+1)/2  c.3/5,4/5 d.none of these Please provide the answer with solution...

Expert Answers

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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:





`==>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.


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`

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