The point $(p, q)$ is on the line $y=\frac{2}{5} x$, as shown. Also, the area of the rectangle shown is 90 . What is the value of $p$ ?
(A) 12
(B) 9
(C) 10
(D) 15
(E) 30

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-069.jpg?height=420&width=477&top_left_y=1351&top_left_x=1298)
Since $(p, q)$ lies on the line $y=\frac{2}{5} x$, then $q=\frac{2}{5} p$.

The given rectangle has two sides on the axes, so has width $p$ and height $q$.

Therefore, the area of the rectangle equals $p q=p \cdot \frac{2}{5} p=\frac{2}{5} p^{2}$.

Since we are told that the area of the rectangle is 90 , then $\frac{2}{5} p^{2}=90$ or $p^{2}=\frac{5}{2}(90)=225$.

Since $p>0$, then $p=\sqrt{225}=15$.

ANSWER: (D)