SOLUTION: A triangle has side lengths measuring 30, 40, and 50 units. What is the length of its shortest altitude, in units?

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Question 909429: A triangle has side lengths measuring 30, 40, and 50 units. What is the length of its shortest altitude, in units?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A triangle has side lengths measuring a=30, b=40, and c=50 units is an right angle triangle.
In a right triangle the three altitudes are: h%5Ba%5D, h%5Bb%5D%2C+and+%7B%7B%7Bh%5Bc%5D (the first two of which equal the leg lengths a and b respectively) and they are related according to

1%2Fh%5Ba%5D%5E2%2B1%2Fh%5Bb%5D%5E2=1%2F+h%5Bc%5D%5E2
plug in h%5Ba%5D=30 and h%5Bb%5D=40
and find h%5Bc%5D
1%2F30%5E2%2B1%2F40%5E2=1%2F+h%5Bc%5D%5E2
1%2F900%2B1%2F1600=1%2F+h%5Bc%5D%5E2
1600%2F1440000%2B900%2F1440000=1%2F+h%5Bc%5D%5E2
%281600%2B900%29%2F1440000=1%2F+h%5Bc%5D%5E2
25cross%280%29cross%280%29%2F14400cross%280%29cross%280%29=1%2F+h%5Bc%5D%5E2

25%2F14400=1%2F+h%5Bc%5D%5E2
cross%2825%291%2Fcross%2814400576%29=1%2F+h%5Bc%5D%5E2

1%2F576=1%2F+h%5Bc%5D%5E2
h%5Bc%5D%5E2=576
h%5Bc%5D=sqrt%28576%29
h%5Bc%5D=24 ...so, this is the length of shortest altitude