Question:
The length of one leg of a right triangle is 9 meters. The lengths of the other two sides are consecutive integer numbers of meters. What is the number of meters in the perimeter of the triangle?

Answer:
By the Pythagorean theorem, we have \begin{align*}
9^2+x^2&=(x+1)^2 \implies \\
81+x^2&=x^2+2x+1 \implies \\
2x&=80 \implies \\
x&=40,
\end{align*}where $x$ is the shorter missing side.  It follows that the sides of the triangle are 9, 40, and 41 meters, and the perimeter of the triangle is $9+40+41=\boxed{90}$ meters.

Note: for any odd integer $n$, the two integers closest to $n^2/2$ along with $n$ form a Pythagorean triple.