Let \( \mathrm{S} \) be the set of all triangle in the \( x y \) - plane, each having one vertex...
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Let \( \mathrm{S} \) be the set of all triangle in the \( x y \) - plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in \( S \) has area \( 50 \mathrm{sq} \). units, then the number of elements in the set \( S \) is:
(1) 9
(2) 18
(3) 32
(4) 36
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