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Problem 386

Geometry Difficulty 2.5 Multiple choice CEMC Fermat · Canada · 2019

In the diagram, each line segment has length $x$ or $y$ . Also, each pair of adjacent sides is perpendicular.

If the area of the figure is 252 and $x=2y$ , the perimeter of the figure is

Pick one

Official solution

Since $x=2y$ , then by drawing dotted lines parallel to the line segments in the given figure, some of which start at midpoints of the current sides, we can divide the figure into 7 squares, each of which is $y$ by $y$ .

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Since the area of the given figure is 252, then $7y^2 = 252$ or $y^2 = 36$ .

Since $y>0$ , then $y = 6$ .

The perimeter of the figure consists of 16 segments of length $y$ .

Therefore, the perimeter is $16 \times 6 = 96$ .

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