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.