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# Triangles with rational area

## Question

A triangle has side lengths a, b and c. We are told that its area is rational.

Which of the following can we conclude about its sides?

1. All three sides are rational
2. Two of the sides are rational, the third is not.
3. One side is rational, the other two are not.
4. None of the sides is rational.
5. All of the above are possible.

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5. All of the above are possible. Here is how:

1. Pythagorean traingle with sides 3, 4, 5.
2. A triangle formed by three verices of a unit square.
3. Two triagles as above glued along short side.
4. Equilateral triangle with unit area.

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I`ll go with the 5th. option.

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