The side lengths of a triangle are 14 cm, 48 cm and 50 cm. How many square centimeters are in the area of the triangle?
Shrinking the triangle by dividing every side length by 2, we recognize the resulting set $$\{7,24,25\}$$ of side lengths as a Pythagorean triple.  Therefore, the original triangle is also a right triangle, and its legs measure 14 cm and 48 cm.  The area of the triangle is $\frac{1}{2}(14\text{ cm})(48\text{ cm})=\boxed{336}$ square centimeters.