tmua.me Extreme Set A Paper 2 · Question 11

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tmua.me Extreme Set A Paper 2 · Q11

Paper 2GeometryNumber & counting

A right-angled triangle has positive integer side lengths $a<b<c$ and area $60$ . Let $h$ be the perpendicular distance from the right-angled vertex to the hypotenuse.

What is the largest possible value of

\frac{h}{b-a}\,?

\dfrac{60}{119}

\dfrac{120}{289}

\dfrac{120}{119}

\dfrac{120}{17}

\dfrac{30}{\sqrt{61}}

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