SOLUTION: if the median to the hypotenuse of a right triangle measures 25 and a leg 14, find the measure of the other leg

Question 292544: if the median to the hypotenuse of a right triangle measures 25 and a leg 14, find the measure of the other leg
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Use the Pythagorean theorem,

where A, B are the legs, H is the hypotenuse.

Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website!
The other tutor's answer is incorrect.
Given triangle ACB is a right triangle and D is the midpoint of AB.
CD = 25

Draw DE perpendicular to AC

Triangle DEB is similar to triangle ACB.
So since D is the midpoint of AB, DB=AB,
So, DE=AC = (14) = 7. So we mark DE
as having length 7:

Next we use the Pythagorean theorem on right triangle DEC to find
the length of CE:

so we mark CE as 24:

Since triangle DEB is similar to triangle ACB, and DB is half of AB,
BE is half of BC, which makes BE = CE = 24. So we label BE as 24 also:

So that makes the other leg BC = 24+24 = 48.
Edwin
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