SOLUTION: the hypotenuse of a right triangle is 20 inches. one of the legs has a meadure of 16 inches. what is the measure of the other leg? the answer i got was not an option

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Question 252631: the hypotenuse of a right triangle is 20 inches. one of the legs has a meadure of 16 inches. what is the measure of the other leg?
the answer i got was not an option
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are x and 16 this means that a=x and b=16


Also, since the hypotenuse is 20, this means that c=20.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2B16%5E2=20%5E2 Plug in a=x, b=16, c=20


x%5E2%2B256=20%5E2 Square 16 to get 256.


x%5E2%2B256=400 Square 20 to get 400.


x%5E2=400-256 Subtract 256 from both sides.


x%5E2=144 Combine like terms.


x=sqrt%28144%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=12 Simplify the square root.


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Answer:


So the solution is x=12 which means that the measure of the remaining leg is 12 inches.