In the diagram, points $P, Q, R$, and $S$ are at intersections of gridlines in a $6 \times 6$ grid. What is the perimeter of parallelogram $P Q R S$ ?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-009.jpg?height=306&width=379&top_left_y=1492&top_left_x=1315)
Since the given grid is $6 \times 6$, the size of each of the small squares is $1 \times 1$.

This means that $Q R=P S=3$.

Join $Q$ to $S$.

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-013.jpg?height=315&width=382&top_left_y=363&top_left_x=926)

Since $Q S$ is vertical, and $Q R$ and $P S$ are both horizontal, then $\angle R Q S=90^{\circ}$ and $\angle P S Q=90^{\circ}$. We note further that $Q S=4$.

Since $\triangle R Q S$ is right-angled at $Q$, by the Pythagorean Theorem,

$$
R S^{2}=Q R^{2}+Q S^{2}=3^{2}+4^{2}=25
$$

Since $R S>0$, then $R S=5$.

Similarly, $P Q=5$.

Thus, the perimeter of $P Q R S$ is $P Q+Q R+R S+P S=5+3+5+3=16$.

ANSWER: $(\mathrm{C})$