SOLUTION: The hypotenuse of a right triangle is 25. If the altitude from the right angle to the hypotenuse is 12, what is the length of the longest segment it forms on the hypotenuse?
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Question 305638: The hypotenuse of a right triangle is 25. If the altitude from the right angle to the hypotenuse is 12, what is the length of the longest segment it forms on the hypotenuse?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
And with a tip of the hat to Mr. Pythagoras we begin:
which is to say:
Then
and
^2)
Which expands to:
Substituting:
and simplifying
but since
we can say:
But then we can write:
and in standard form:
which factors to
(x\ -\ 16)\ =\ 0)
So
or
which is the situation if the diagram was turned over. Since the question asks for the longer of the two segments, the answer is 16.
John
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