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Triangle ABC has altitudes AD, BE, and CF. AD=12cm and BE=14cm. Find the largest possible value for CF if CF is an integer.

 Jun 1, 2020
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Let h be the third altitude.  Then by the triangle inequality, h + 12 > 14, h + 14 > 12, and 12 + 14 > h.  The largest integer h that satisfies these inequalities is h = 25.

 Jun 1, 2020

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