Find the lengths of the other two sides.

Question

The shortest side of a right triangle measure 7m.The lengths of the other two sides are conservative integers.Find the lengths of the other two sides.

Answer 1

Assuming X denotes the length of the second leg (Cathetus) of the right triangle, the equation applying Pythagorean Theorem:

7² + X² = (X+1)²

Simplify

49 + X² = X²+2X+1

2X=48

Solve: X=24 (length of the second Cathetus) and the length of Hypotenuse is equal 25

Answer 2

n = length of the shorter of the other sides

n + 1 = length of the longer of the other sides

 

Note that the side of length n + 1 must be the hypotenuse of the right triangle.  Then

 

7² + n² = (n + 1)²

 

49 + n² = n² + 2n + 1

 

49 = 2n + 1

 

n = (49 - 1)/2 = 24

 

n + 1 = 25

 

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