A rectangle has width and length , as shown in Figure 1. The rectangle is cut along the horizontal and vertical dotted lines in Figure 1 to produce four smaller rectangles as shown in Figure 2.
The sum of the perimeters of these four rectangles in Figure 2 is . The value of is
, 2024
Pick one
Solution
The sum of the lengths of the horizontal line segments in Figure
2 is , because the tops of the four small rectangles contribute a total of to their combined perimeter and the bottoms of the four small rectangles contribute a total of to their combined perimeter. Similarly, the sum of the lengths of the vertical line segments in Figure 2 is . In other words, the sum of the perimeters of the four rectangles in Figure 2 is . Since the sum of the perimeters also equals , then and so .
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