In the diagram, $\triangle P Q R$ is equilateral and is made up of four smaller equilateral triangles. If each of the smaller triangles has a perimeter of $9 \mathrm{~cm}$, what is the perimeter of $\triangle P Q R$ ?
(A) $15 \mathrm{~cm}$
(B) $9 \mathrm{~cm}$
(C) $36 \mathrm{~cm}$
(D) $27 \mathrm{~cm}$
(E) $18 \mathrm{~cm}$

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-028.jpg?height=276&width=325&top_left_y=2125&top_left_x=1320)

Part B: Each correct answer is worth 6.
Each of the 4 smaller triangles is equilateral and thus has sides of equal length.

Each of these smaller triangles has a perimeter of $9 \mathrm{~cm}$ and so has sides of length $\frac{9}{3}=3 \mathrm{~cm}$.

In $\triangle P Q R$, side $P Q$ is made up of two such sides of length $3 \mathrm{~cm}$ and thus $P Q=2 \times 3=6 \mathrm{~cm}$. Since $\triangle P Q R$ is equilateral, then $P R=Q R=P Q=6 \mathrm{~cm}$.

Therefore, the perimeter of $\triangle P Q R$ is $3 \times 6=18 \mathrm{~cm}$.

ANSWER: (E)