SOLUTION: Here is the problem in exact words. 3,4,5 and 7,24,25 are examples of a Pythagorean Triple. Pythagorean Triples are made up of whole numbers. These two examples are special becau

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Here is the problem in exact words. 3,4,5 and 7,24,25 are examples of a Pythagorean Triple. Pythagorean Triples are made up of whole numbers. These two examples are special becau      Log On

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Question 129112This question is from textbook ALGEBRA 1
: Here is the problem in exact words.
3,4,5 and 7,24,25 are examples of a Pythagorean Triple. Pythagorean Triples are made up of whole numbers. These two examples are special because in both cases the hypotenuse is 1 greater than the longer leg.
Find one where one of the legs is 37 and the hypotenuse is one more than th longer leg.
I really need help with this. Please try to get back to me as soon as possible. This question is from textbook ALGEBRA 1

Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
There are two possibilities:

First, the longer leg could be 37, then the hypotenuse is 38, and the shorter leg is the square root of 38%5E2-37%5E2. 38%5E2-37%5E2=1444-1369=75. Since 75 is not a perfect square, this is not the correct answer.

The other possibility is that 37 is the short leg, x is the long leg, and x + 1 is then the hypotenuse. Using Pythagoras:

%28x%2B1%29%5E2=x%5E2%2B37%5E2
x%5E2%2B2x%2B1=x%5E2%2B1369
2x%2B1=1369
2x=1368
x=684

So the Pythagorean triple is 37, 684, 685. I'll leave it as a exercise for you to do the arithmetic and prove it.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find one where one of the legs is 37 and the hypotenuse is one more than the longer leg.
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(x+1)^2 = x^2+ 37^2
2x+1 = 37^2
2x = 1368
x = 684 (2nd leg)
x+1 = 685 (hypotenuse)
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Cheers,
Stan H