Use $\sin 45^\circ = \frac{\text{opposite}}{\text{hypotenuse}}$ or $\cos 45^\circ = \frac{\text{adjacent}}{\text{hypotenuse}}$ with hypotenuse $16$.

A right triangle with a $45^\circ$ acute angle has two equal legs. Add the hypotenuse and both legs to get the perimeter.

In Desmos settings, set the angle unit to degrees.

Enter L = 16*sin(45) (or 16*cos(45)) to compute the leg length.

Enter P = 16 + 2L to compute the perimeter.

Compare your value (or its radical form) to the listed choices and select the matching expression.

The longest side is the hypotenuse, so its length is $16$.

Using $\sin 45^\circ = \frac{\text{leg}}{\text{hypotenuse}}$:

In a right triangle with one acute angle $45^\circ$, the other acute angle is also $45^\circ$, so the two legs are equal.

Perimeter:

Combine like terms:

So, the perimeter of the sail is $16+16\sqrt{2}$.