2002 AMC 10A Problem 13

Problem 13 of 25IntermediateGeometry

The sides of a triangle have lengths of

15,

20,

and

25.

Find the length of the shortest altitude.

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Solution

Since

15^2+20^2=225+400

=625=25^2,

the triangle is right with legs

15

and

20,

and area

\dfrac{1}{2}(15)(20)=150.

The shortest altitude falls to the longest side

25,

and equals

\dfrac{2\cdot 150}{25}=12.

Thus, the correct answer is B.

Concepts: right triangle · altitude · triangle area

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.