SOLUTION: Suppose a right triangle has two legs, one of length 5 and the other of length 3. What is the length of the hypotenuse? Please show work.

Algebra ->  Pythagorean-theorem -> SOLUTION: Suppose a right triangle has two legs, one of length 5 and the other of length 3. What is the length of the hypotenuse? Please show work.      Log On


   

Question 243575: Suppose a right triangle has two legs, one of length 5 and the other of length 3. What is the length of the hypotenuse? Please show work.
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 3 and 5 this means that a=3 and b=5


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


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


3%5E2%2B5%5E2=x%5E2 Plug in a=3, b=5, c=x


9%2B5%5E2=x%5E2 Square 3 to get 9.


9%2B25=x%5E2 Square 5 to get 25.


34=x%5E2 Combine like terms.


x%5E2=34 Rearrange the equation.


x=sqrt%2834%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%2834%29 which approximates to x=5.831.


So the hypotenuse is approximately 5.831 units long.