one leg of a right triangle has a length of 7m the other sides have lengths that are consecutive integers. find these lengths

Question

one leg of a right triangle has a length of 7m the other sides have lengths that are consecutive integers. find these lengths. 

Answer 1

Since it's a right triangle, you can say 7² + L² = H², where L is the other leg and H is the hypotenuse.

 

L and H are consecutive integers, and since the hypotenuse is always larger than both legs, H must be the larger integer.  So H = L + 1.

 

Substitute L+1 for H in the original equation:

 

49 + L² = (L + 1)²

49 + L² = L² + 2L + 1

49 = 2L + 1

48 = 2L

24 = L

 

So H = 25