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Problem of the Week
Problem C
A Rectangle of Rectangles

Large rectangle \(JKLM\) is formed by twelve identical smaller rectangles, as shown.

5 smaller rectangles are stacked on top of each other. Their combined widths form side JM of the large rectangle. A sixth smaller rectangle is to the right of the stack and arranged so that its length is adjacent to the widths of the 5 stacked rectangles. To its right, this arrangement of 6 rectangles is repeated.

If the area of \(JKLM\) is \(540\text{ cm}^2\), then determine the dimensions of the smaller rectangles.

Themes: Algebra, Geometry & Measurement