Question 217386: The sides of a triangle are 15, 20, and 25. What is the length of the shortest altitude?
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Checking, we find that 15^2 +20^2 =25^2,,,,therefore this is a rt triangle, with legs 15, and 20, and hypotenuse 25
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On a right triangle, the legs are also altitudes, so 15, and 20 are altitudes.
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We need to check the altitude from the hypotenuse to the opposite vertex, however.
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Perhaps the easiest way is to establish the Area of the triangle, and then calculate that altitude.
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Area = 1/2 *b*h,,,and for square legs,,,A= 1/2*15*20 = 150
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For the hypotenuse as a base,,A= 1/2 *b*h,,,,150 = 1/2 *25 *h,,,h=12
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As it turns out, this last altitude is the smallest,,,,,,12
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