Represent the hypotenuse of a right triangle by c and the area by A. The altitude on the hypotenuse is:

\frac{A}{c}

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\frac{2 A}{c}

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\frac{A}{2 c}

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\frac{A^{2}}{c}

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\frac{A}{c^{2}}

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Solution

The correct option is B $\frac{2 A}{c}$
Let a, b be the two sides of triangle other than hypotenuse.
$\frac{1}{2} a b = A ⟹ a b = 2 A ⟹ a^{2} + b^{2} = c^{2} ⟹ \frac{1}{2} h c = \frac{1}{2} a b ⟹ h c = 2 A ∴ h = \frac{2 A}{c}$

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