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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!

Comments

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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1 Answer

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)