IMC 2004 Q15

As triangle A has two equal sides, it should have two equal angles, but its angles are 25°, 110° and 45° so it is impossible to make. In a triangle, the smallest angle lies opposite the shortest side which makes B impossible since 20° is the smallest angle, but 5 cm is not the shortest side. Triangle C is impossible as 4² + 7² ≠ 8², so it does not obey Pythagoras' Theorem. The longest side of a triangle must be shorter than the sum of the other two sides, but this is not the case in triangle E, so it cannot be made either. Triangle D, however, is obtained by cutting an equilateral triangle of side 6 cm in half along an axis of symmetry and so can certainly be made.