The shortest side of a right triangle measures 11m. the lengths of the other two sides are consecutive integers. find the lengths of the other two sides.

Interesting question.  Let the 2 unknown sides be x and x+1.
Then (11 m)^2 + x^2    = sum of the squares of the 2 shortest sides
                                     = (x+1)^2

121 + x^2 = x^2 + 2x + 1.  Then 121 = 2x + 1, and 2x = 120, or x = 60.

Then the hyp. has length 60+1= 61.

We must check these results.  Using the Pyth. Thm. (a^2 + b^2 = c^2),

11^2 + 60^2 = 61^2
121 + 3600 =  3721     This is true, so our answers are correct.

The longer side is 60 and the hyp. has length 61.