A rectangle with height $x$ and width $2 x$ has the same perimeter as an equilateral triangle with side length 10 . What is the area of the rectangle?
![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-033.jpg?height=262&width=618&top_left_y=1430&top_left_x=714)
(A) 18
(B) 50
(C) 25
(D) 200
(E) 100
Since the given equilateral triangle has side length 10 , its perimeter is $3 \times 10=30$.

In terms of $x$, the perimeter of the given rectangle is $x+2 x+x+2 x=6 x$.

Since the two perimeters are equal, then $6 x=30$ which means that $x=5$.

Since the rectangle is $x$ by $2 x$, its area is $x(2 x)=2 x^{2}$.

Since $x=5$, its area is $2\left(5^{2}\right)=50$.

ANSWER: (B)