1955 AMC 12 Problem 21

Attempt Problem 21 of the 1955 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1955 AMC 12 solutions, or check the answer key.

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21.

Represent the hypotenuse of a right triangle by

c

and the area by

A.

The altitude on the hypotenuse is:

\dfrac Ac

\dfrac{2A}{c}

\dfrac A{2c}

\dfrac{A^2}{c}

\dfrac A{c^2}

Use the hypotenuse as the base of the triangle

If the corresponding altitude is

h,

then

A=\frac{ch}{2}

Taking the hypotenuse as the base and writing its altitude as

h,

A=\frac12ch.

Solving gives

h=\frac{2A}{c}.

Thus, the correct answer is B.

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