Problem in the ACoPS [Maths]

Given a point (a,b) with 0 < b < a, determine the minimum perimeter of a triangle with one vertex at (a,b), one on the x-axis, and one on the line y = x. You may assume that a triangle of minimum perimeter exists.

Try exploiting symmetry.

point on x-axis: (x1,0)
point on x = y:  (x2,x2)

Then p = sqrt((a-x1)^2 + b^2) + sqrt((x2-a)^2 + (x2 - b)^2) + sqrt((x1-x2)^2 + x2^2)

constraints, 0 < x1 < a; 0 < x2 < a

solve using technology.

Why must x1, x2 be less than a? Isn't it only true that (a,b) must be between both y = x and the x-axis, and that it could be leftwards of the other two vertices.

oh i guess it doesn't

but anyways you need an x1, x2 to minimize that equation rite?

Yes, you do.

You could set the constraints: 0 < b < x2, 0 < b < a

The actual answer should be much simpler from what you got before.