A triangle of consecutive integers

The three side lengths of a triangle and one of its heights (altitudes) are four consecutive whole numbers, in some order. What is the area of the triangle?

Show hints (2)+
  1. An altitude is shorter than the two sides it isn't perpendicular to - so it's likely the smallest of the four numbers.
  2. Test the famous 1313-1414-1515 triangle: its altitude to the side 1414 is 1212. Compute its area with Heron.

Answer

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84

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Asked at: Jane Street, Optiver

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