Find the length of the shortest altitude in a triangle with sides 5, 12, 13.
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
13h = 60
h = 60/13 = 4.61
This one has a sneaky answer . . .
We note that: .5² + 12² .= .13² . . . It is a right triangle!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.)