Let $x$ be the length of the unknown leg. Which side is the hypotenuse (the longest side, opposite the right angle), and how does it appear in the Pythagorean formula $c^2 = a^2 + b^2$?

Once you write $13^2 = 5^2 + x^2$, move $5^2$ to the other side. What is $13^2$? What is $5^2$? Subtract to find $x^2$.

After you find $x^2$, remember that $x$ is the positive square root of that number, because $x$ is a side length.

In a Desmos expression line, type sqrt(13^2 - 5^2) to represent the length of the unknown leg.

Look at the numerical value that Desmos returns for this expression; that value is the length of the other leg in meters.

You are told the triangle is a right triangle.

• The hypotenuse (the side opposite the right angle) has length $13$.
• One leg has length $5$.
• You need to find the length of the other leg.

For a right triangle with legs $a$ and $b$ and hypotenuse $c$, the Pythagorean theorem says:

Let the unknown leg be $x$. Here, $c = 13$ and one leg is $5$, so:

Now solve for $x^2$:

Compute the squares:

So:

You found that $x^2 = 144$. To get $x$, take the positive square root (lengths are positive):

The square root of $144$ is $12$, so the other leg is $12$ meters long. That corresponds to choice C.