SOLUTION: if the length of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse?

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Question 592875: if the length of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse?
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 5 and 7 this means that a=5 and b=7


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


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


5%5E2%2B7%5E2=x%5E2 Plug in a=5, b=7, c=x


25%2B7%5E2=x%5E2 Square 5 to get 25.


25%2B49=x%5E2 Square 7 to get 49.


74=x%5E2 Combine like terms.


x%5E2=74 Rearrange the equation.


x=sqrt%2874%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


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Answer:


So the solution is x=sqrt%2874%29 which approximates to x=8.602.


So the hypotenuse is roughly 8.602 units long.