Find the length of the shortest altitude in a triangle with sides 5, 12, 13.

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- April 28th 2007, 05:45 PMjumpman23triangles
Find the length of the shortest altitude in a triangle with sides 5, 12, 13.

- April 28th 2007, 06:05 PMThePerfectHacker

This is a right triangle.

Thus, 5 and 12 are two of its altitutes

But it is not the smallest.

The smallest is the one drawn from intersection of 5 and 12to hypotenuse.

Let h be that length.

Then, (13h)(1/2) = Area

But, Area = (1/2)(5)(12) = 30

Thus,

13h = 60

h = 60/13 = 4.61 - April 28th 2007, 06:07 PMSoroban
Hello, jumpman23!

This one has a*sneaky*answer . . .

Quote:

Find the length of the shortest altitude in a triangle with sides 5, 12, 13.

Therefore, the shortest altitude is 5.

(Make a sketch and you'll see it.)