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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.
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.
Hello, gfbrd!
Did you make a sketch?
Quote:
Give 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.
PointCode:|
| *
| *
| R *
| o(y,y)
| ** *
| * * *
| * * * P
| * * o(a,b)
| * * *
| * * *
| * Q * *
- - * - - - o - - - - - - - - - - - -
| (x,0)
|
has given coordinates
It lies below the 45o-line.
Pointlies on the x-axis with coordinates
Pointlies on the line
with coordinates
The lengths of the sides of the triangle are:
. .
. .
. .
The perimeter of the triangle is:
. .
And that is the function we must minimize.
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.