Twenty-nine is the shortest leg of a right triangle whose other leg and hypotenuse are consecutive whole numbers. What is the sum of the lengths of the other two sides?

Call the other leg is: x

So the hypotenuse is x + 1

We have: \(29^2+x^2=\left(x+1\right)^2\)( Pythagorean theorem)

\(\Leftrightarrow841+x^2=x^2+2x+1\)

\(\Leftrightarrow841=2x+1\)

\(\Leftrightarrow x=420\)

=> The sum of two sides is: 420 + 29 = 449