<PRE><B>Question 288311</B>
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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