SOLUTION: TEWNTY NINE IS THE SHORTEST LEG OF A RIGHT ANGLED TRIANGLE THE HYPOTENUS AND OTHER LEG ARE TWO CONSECUTIVE WHOLE NUMBERS. WHAT ARE THE LENGHTS OF THE LEG AND HYPOTENUS

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Question 167456: TEWNTY NINE IS THE SHORTEST LEG OF A RIGHT ANGLED TRIANGLE THE HYPOTENUS AND OTHER LEG ARE TWO CONSECUTIVE WHOLE NUMBERS. WHAT ARE THE LENGHTS OF THE LEG AND HYPOTENUS
Found 2 solutions by Mathtut, checkley77:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2%2Bb%5E2=c%5E2-eq where we will call a the shortest leg, b the other leg,and c the hypothenuse. Lets call b=b and c=b+1 where b and b+1 are two consecutive whole numbers. no substitute our known numbers and variables into the equation.
29%5E2%2Bb%5E2=%28b%2B1%29%5E2 solving we have 841%2Bb%5E2=b%5E2%2B2b%2B1
2b=840 highlight%28b=420%29other leg highlight%28c=420%2B1=421%29 hypothenuse

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
29^2+x^2=(x+1)^2
841+x^2=x^2+2x+1
2x+1-841=0
2x=841-1
2x=840
x=840/2
x=420 for the other side.
420+1=421 is the length of the hypotenuse.
Proof:
29^2+420^2=421^2
841+176,400=177,241
177,241=177,241