1986 AHSME Problems/Problem 11
Contents
[hide]Problem
In and . Also, is the midpoint of side and is the foot of the altitude from to . The length of is
Solution
In a right triangle, the length of the hypotenuse is twice the length of the median which bisects it. If the hypotenuse is , the median must be .
Solution 2 (Self Torture)
Warning: this solution is very intensive in calculation. Please do NOT try this on the test!
Let's start by finding . By Heron's Formula, . Using the area formula , . Now using the Pythagorean Theorem, .
Now . Using Stewart's Theorem on , letting :
(remember that Stewart's Theorem is ).
Thus or (reject this solution since is positive). Thus . Select .
~hastapasta
P.S.: Although this is torturous, this is a good practice of Heron's formula and Stewart's theorem though.
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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