SOLUTION: the altitude of a right triangle splits the hypotenuse into two segments of length 4 and 16. what is the length of the altitude?

Question 288311: the altitude of a right triangle splits the hypotenuse into two segments of length 4 and 16. what is the length of the altitude?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Let x and y be the two legs of the rigth triables and a be the altitute. The altitute a creates two more right triable, one with sides a, 4 and hypotenuse y and theother with sdes a, 16 and hypotenuse x.
From the Pythagorean Theorem we have then:
x^2 + y ^2 = (16 + 4)^2 or
1.) x^2 + y^2 = 400
We also have:
2.) y^2 = a^2 + 4^2 and
3.) x^2 = a^2 + 16^2
Adding the two equations above we have:
x^2 + y^2 = 2*a^2 + 4^2 + 16^2 or
4.) x^2 + y^2 = 2*a^2 + 272
From 1.) we have x^2 + y^2 = 400 so 4.) becomes:
400 = 2*a^2 + 272
2*a^2 = 400 - 272
2*a^2 = 128
a^2 = 64
a = sqrt(64)
a = 8

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