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Algebra Difficulty 2.5 Junior Find the answer Canada

A rectangle has width $x$ and
length $y$ , 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
$24$ . The value of $x + y$ is

Pick one

Solution

The sum of the lengths of the horizontal line segments in Figure
2 is $4x$ , because the tops of the
four small rectangles contribute a total of $2x$ to their combined perimeter and the
bottoms of the four small rectangles contribute a total of $2x$ to their combined perimeter.

Similarly, the sum of the lengths of the vertical line segments in
Figure 2 is $4y$ .

In other words, the sum of the perimeters of the four rectangles in
Figure 2 is $4x + 4y$ .

Since the sum of the perimeters also equals $24$ , then $4x +
4y = 24 $and so$ x + y =
6$.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.