The coordinates of the vertices of rectangle $P Q R S$ are given in the diagram. The area of rectangle $P Q R S$ is 120 . The value of $p$ is
(A) 10
(D) 14
(B) 12
(E) 15
(C) 13

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-096.jpg?height=353&width=504&top_left_y=932&top_left_x=1277)
The coordinates of the vertices of rectangle $P Q R S$ are given in the diagram. The area of rectangle $P Q R S$ is 120 . The value of $p$ is
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-430.jpg?height=351&width=512&top_left_y=1123&top_left_x=1289)

## Solution 1

$P S=12-2=10$

Since the area of the rectangle is 120 ,

$$
\begin{aligned}
(P S)(P Q) & =120 \\
(10)(P Q) & =120 \\
P Q & =12
\end{aligned}
$$

Therefore, $p=3+12=15$.

## Solution 2

The dimensions of the rectangle are $(p-3) \times 10$.

Since the area is $120,10(p-3)=120$.

Thus, $p-3=12$

or $p=15$.

ANSWER: (E)