MathDB

Let

T

be an acute triangle. Inscribe a rectangle

R

T

with one side along a side of

T.

Then inscribe a rectangle

S

in the triangle formed by the side of

R

opposite the side on the boundary of

T,

and the other two sides of

T,

with one side along the side of

R.

For any polygon

X,

let

A(X)

denote the area of

X.

Find the maximum value, or show that no maximum exists, of

\tfrac{A(R)+A(S)}{A(T)},

where

T

ranges over all triangles and

R,S

over all rectangles as above.

Problem Statement