SOLUTION: 2. The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is 5 cm. Find the length of the other leg. (1 point) 14 cm 144 cm 8 cm 12 cm

Algebra ->  Linear-equations -> SOLUTION: 2. The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is 5 cm. Find the length of the other leg. (1 point) 14 cm 144 cm 8 cm 12 cm      Log On


   

Question 669007: 2. The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is 5 cm. Find the length of the other leg. (1 point)
14 cm
144 cm
8 cm
12 cm
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 x this means that a=5 and b=x


Also, since the hypotenuse is 13, this means that c=13.


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


5%5E2%2Bx%5E2=13%5E2 Plug in a=5, b=x, c=13


25%2Bx%5E2=13%5E2 Square 5 to get 25.


25%2Bx%5E2=169 Square 13 to get 169.


x%5E2=169-25 Subtract 25 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.