SOLUTION: the lengths of the sides of a right triangle are given by three consecutive integers. find the lengths of all three sides

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Question 1170475: the lengths of the sides of a right triangle are given by three consecutive integers. find the lengths of all three sides
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
3, 4, 5;
3%5E2%2B4%5E2=5%5E2
9%2B16=25
25=25

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3, 4, 5
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if we have n+as the first integer, then n%2B1+will be the second integer,+n%2B2 will be the third integer
the lengths of the sides of a right+triangle are given by three consecutive integers so that
n+ and n%2B1+ are legs
+n%2B2 hypothenuse
+%28n%2B2%29%5E2=n%5E2%2B%28n%2B1%29%5E2 .......solve for n+
+n%5E2%2B4n%2B4=n%5E2%2Bn%5E2%2B2n%2B1
+n%5E2%2B4n%2B4=2n%5E2%2B2n%2B1
+0=2n%5E2-n%5E2-4n%2B2n%2B1-4
+0=n%5E2-2n-3
+0=n%5E2%2Bn-3n-3
+0=%28n%5E2%2Bn%29-%283n%2B3%29
+0=n%28n%2B1%29-3%28n%2B1%29
+0=%28n-3%29%28n%2B1%29
solutions:
n=3
n=-1...disregard negative solution
the lengths of all three sides:
3, 4+, and +5