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One leg of a right triangle has a length of 7ft. The other sides have lengths that are consecutive integers.find these lengths

Please explain the process not just the answer. Thank you!

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Hi Jay!  An interesting pattern emerges: square the given side, subtract by one, and cut in half ... given 5, 25-1 is 24, cut in half to 12 ===> 5,12,13 triangle.  This "all-integer" triangle "recipe" works only for an odd given side. How 'bout given 9? 81-1 is 80, cut in half to 40 ==> 9,40,41; next is 11,60,61 Best regards :) 

Hi Brad, that idea is good one!!

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Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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Let's assume that length of the second leg is x ft, then length of the hypotenuse is (x + 1) ft.
Now, let's apply the Pythagorean theorem: (x + 1)2 = x2 + 72
x2 + 2x + 1 = x2 + 49
2x = 48 ---> x = 24 ft (second leg)
              x + 1 = 25 ft (hypotenuse)