Maximum perimeter of triangle in a rectangle

Question

What is the maximum perimeter of a triangle that is inscribed in a rectangle? Prove your claim

I found this problem while formulating the question of maximum length of rod that a truck can carry with the shape of wire being an arbitary curve.... I started off as a triangle for simplicity... I have deduced that the services must touch the sides of the rectangle...My progress is on...(to be posted soon)

Can someone generalise it to a arbitary curve.. – MATHS MOD Mar 04 '19 at 10:59 — MATHS MOD, Mar 04 '19 at 10:59

score 1 · Accepted Answer · answered Mar 04 '19 at 10:56

Observe that you never decrease the perimeter if you push a triangle vertex towards one of the rectangle vertices. Thus, the maximum is achieved when the three triangle vertices are three of the four rectangle vertices. The maximal diameter is $a+b+\sqrt{a^2+b^2},$ if $a$ and $b$ are the sides of the rectangle.

Maximum perimeter of triangle in a rectangle

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