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Homelargest area rectangle

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# largest area rectangle

LaTeX field for this problem:

What must be the ratio of the sides of a right triangle to make its area a maximum, if the hypothenuse is constant?

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## Comments

## square a/b=1

square a/b=1

## It must be a ratio of 1:1

If the ratio was not $1:1$ then two identical triangles could be assembled to make a non-square rectangle. But a square is the maximal shape for a rectangle.