How many units are in the sum of the lengths of the three altitudes in a triangle with sides 5, 12, and 13?
+2666 Note that we have a right triangle, because \(5^2 + 12^2 = 13^2 \)
This means that 2 of the altitudes are 5 and 12 because they are perpendicular to another side.
The third altitude can be found with this formula: \(\text{hypotenuse} \times \text{altitude} \div 2 = \text{Area}\).
We know the area is 30 and the hypotenuse is 13, meaning the altitude is \({60 \over 13}\).
Can you find the sum from here?
