A square is cut into two identical rectangles, as shown.

![](https://cdn.mathpix.com/cropped/2024_04_30_aeb4d8fddfe5f1048ea8g-2.jpg?height=274&width=628&top_left_y=1717&top_left_x=716)

Each of these two rectangles has perimeter $24 \mathrm{~cm}$. What is the area of the original square?
Suppose that the square has side length $2 x \mathrm{~cm}$.

Each of the two rectangles thus has width $2 x \mathrm{~cm}$ and height $x \mathrm{~cm}$.

In terms of $x$, the perimeter of one of these rectangles is $2(2 x \mathrm{~cm})+2(x \mathrm{~cm})$ which equals $6 x \mathrm{~cm}$.

Since the perimeter of each rectangle is $24 \mathrm{~cm}$, then $6 x=24$ which means that $x=4$.

Since the square has side length $2 x \mathrm{~cm}$, then the square is $8 \mathrm{~cm}$ by $8 \mathrm{~cm}$ and so its area is $64 \mathrm{~cm}^{2}$.

ANSWER: $64 \mathrm{~cm}^{2}$

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