SOLUTION: the hypotenuse of a right triangle measures 29 cm. one leg is 1 cm shorter than the other. what are the lenghts of the legs?

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Question 443094: the hypotenuse of a right triangle measures 29 cm. one leg is 1 cm shorter than the other. what are the lenghts of the legs?
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that a%5E2+%2B+b%5E2+=+c%5E2.
We know that c+=+29 and we know that one of the legs is 1 less than the other. Let's choose a to be 1 less than b.
Then a+=+b-1
%28b-1%29%5E2+%2B+b%5E2+=+29%5E2
%28b-1%29%2A%28b-1%29+%2B+b%5E2+=+29%5E2
b%5E2+-b+-b+%2B1++%2Bb%5E2+=+29%5E2
b%5E2+-2b+%2B+1+%2Bb%5E2+=+29%5E2
2b%5E2+-2b+%2B+1+=+841
2b%5E2+-2b+-840
2%2A%28b%5E2+-b+-420%29
2%28b%2B20%29%28b-21%29
So b=-20 or b=21
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But it does not make sense to have a negative length, so the one that makes LOGICAL sense is b =21
If b =21, then a=20 since a = b-1.
So we have (20,21,29) is our triangle.