In the diagram, $A B C D$ is a rectangle with $D C=12$. If the area of triangle $B D C$ is 30 , what is the perimeter of rectangle $A B C D$ ?
(A) 34
(B) 44
(C) 30
(D) 29
(E) 60

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-148.jpg?height=269&width=417&top_left_y=1424&top_left_x=1323)
In the diagram, $A B C D$ is a rectangle with $D C=12$. If the area of triangle $B D C$ is 30 , what is the perimeter of rectangle $A B C D$ ?
(A) 34
(B) 44
(C) 30
(D) 29
(E) 60

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-278.jpg?height=307&width=463&top_left_y=215&top_left_x=1362)

## Solution

Since the area of $\triangle B D C$ is 30 , we know

$$
\begin{aligned}
\frac{1}{2}(12)(B C) & =30 \\
6(B C) & =30 \\
B C & =5
\end{aligned}
$$

Thus, the perimeter of rectangle $A B C D$ is $2(12)+2(5)=34$. ANSWER: (A)