# How can the sides of a triangle be maximised given base and height?

I've encountered a problem in which I want to maximise the lengths of the sides of a triangular structure while still fitting within an area of 220 x 100. This reduces to maximising the lengths of the sides of triangle with base 220 and height 100.

How could the maximised lengths be calculated?

Edit:- Adding clearer bounds to the problem

The triangle must fit in an area bounded by sides of 300 & 100.

• which hight do you mean? – Dr. Sonnhard Graubner Nov 11 '17 at 12:53
• I don't think I bounded my question well enough, I'll edit it to add more bounds. I think @user8734617 may be on the right lines though. – Era Nov 11 '17 at 13:23
• What is the "length"? Do you mean "perimeter"? If so, use the Pythagorean theorem. – user202729 Nov 11 '17 at 13:25
• Just consider that the distance is a convex function, the sum of convex functions is a convex function and convex functions on bounded, convex domains attain their maximum values at the boundary. – Jack D'Aurizio Nov 11 '17 at 14:07