Calculating the Minimum Perimeter of a Triangle

Hey there sorry if this is in the wrong thread, but I need some help with this problem I'm stuck on.

Give a point (a,b) with 0 < b < a

determine the minimum perimeter of a triangle with one vertex at (a,b), on the x-axis,

and one on the line y = x.

I hope someone can help/guide me through this problem, so I can understand how to do this problem thanks.

Re: Calculating the Minimum Perimeter of a Triangle

No triangle exists that minimizes that condition.

However, the infinum of the perimeters of all such triangles = twice the distance from (a,b) to the line y = x.

That's just an application of the triangle inequality after picking the first two points (one is on the line, the other is (a,b)) of any triangle.

Re: Calculating the Minimum Perimeter of a Triangle

Re: Calculating the Minimum Perimeter of a Triangle

Apologies - ignore my previous post - it's wrong. I simply read right over the phrase "on the x-axis", and so didn't include that condition.