How many units are in the sum of the lengths of the three altitudes in a triangle with sides 7, 24 and 25? Express your answer as a decimal to the nearest hundredth.

This is a "Pythagorean Triple" right triangle....

Two of the altitudes are 7 and 24

The third altitude is given by [ 7 * 24] / 25 = 6.72

So the sum of the altitudes is 6.72 + 7 + 24 = 37.72