Use 32 and 18 as the legs in $a^2 + b^2 = c^2$, and let $c$ be the hypotenuse. Write out $32^2 + 18^2$.

After you find $c^2$, remember that $c$ is not $c^2$. You must take the square root and then look for a perfect-square factor to simplify the radical.

In Desmos, type the expression sqrt(32^2 + 18^2) on a new line. Note the decimal value that Desmos gives; this is the hypotenuse length.

On separate lines in Desmos, type 14*sqrt(5), 2*sqrt(337), 50, and 1348. Compare each value to the result of sqrt(32^2 + 18^2) and choose the option whose value matches it exactly.

Because the triangle is a right triangle and you are looking for the hypotenuse, use the Pythagorean theorem:

Here, $a$ and $b$ are the legs (32 and 18), and $c$ is the hypotenuse.

Plug in the given leg lengths:

Now compute each square:

• $32^2 = 1024$
• $18^2 = 324$

So:

Add the squared values:

So you have:

To get $c$, you now need to take the square root of 1348 and simplify the radical.

Take the square root of both sides:

Simplify the radical by factoring out perfect squares:

• Notice that $1348$ has a factor of $4$ (a perfect square): $1348 = 4 \times 337$.
• Therefore,

Thus, the length of the hypotenuse is $2\sqrt{337}$.