A right triangle with a perimeter of 60 units has an altitude (to the hypotenuse) of length 12 units. Find the sum of the lengths of the two (non-hypotenuse) legs of this triangle.
+128473 Call a, b the legs and the hypotenuse, c
a + b + c = 60
a + b = 60 - c square both sides
a^2 + 2ab + b^2 = 3600 - 120c + c^2
Note a^2 + b^2 = c^2
So....we have that
2ab = 3600 - 120c
ab = 1800 - 60c (1)
Area of triangle = (1/2) ab
Also
Area = (1/2)c *12 so
(1/2)ab = (1/2) 12c
ab = 12c (2) sub (1) into (2)
1800 - 60 c = 12c
1800 = 72c
c = 25
a + b = 60 - c
a + b = 60 - 25
a + b = 35 = sum of the leg lengths
