In the diagram, the square has a perimeter of 48 and the triangle has a height of 48 . If the square and the triangle have the same area, what is the value of $x$ ?
(A) 1.5
(B) 12
(C) 6
(D) 3
(E) 24

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-069.jpg?height=260&width=352&top_left_y=2258&top_left_x=1388)

Part C: Each correct answer is worth 8.
Since the perimeter of the square is 48 , its side length is $48 \div 4=12$.

Since the side length of the square is 12 , its area is $12 \times 12=144$.

The area of the triangle is $\frac{1}{2} \times 48 \times x=24 x$.

Since the area of the triangle equals the area of the square, then $24 x=144$ or $x=6$.

ANSWER: (C)

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