A rectangle was divided by two lines, parallel to its sides, into four rectangles. One of them turned out to be a square, and the perimeters of the rectangles adjacent to it are 20 cm and 16 cm. Find the area of the original rectangle.
Let's introduce the notations as shown in the figure. Express the half-perimeters of the rectangles specified in the condition: \(a + x = 8\) and \(b + x = 10\). Then the area of the original rectangle is \((a + x)(b + x) = 80\) (sq units).

![](https://cdn.mathpix.com/cropped/2024_05_06_297c289048f559686628g-28.jpg?height=431&width=512&top_left_y=342&top_left_x=773)

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