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Turkish NMO First Round - 2012 Problem - 01 {Geometry}

Source:

July 1, 2012

geometryperimeterratioarea of a triangleHeron's formula

Problem Statement

Find the perimeter of a triangle whose altitudes are

3,4,

and

6

<span class='latex-bold'>(A)</span>\ 12\sqrt\frac35 \qquad <span class='latex-bold'>(B)</span>\ 16\sqrt\frac35 \qquad <span class='latex-bold'>(C)</span>\ 20\sqrt\frac35 \qquad <span class='latex-bold'>(D)</span>\ 24\sqrt\frac35 \qquad <span class='latex-bold'>(E)</span>\ \text{None}