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Algebra Difficulty 1.2 Junior Find the answer Canada

In the diagram, the lengths of four of the sides of the figure
are shown in terms of $x$ .

Assuming that $x \neq 0$ , the
perimeter of the figure is

Pick one

Solution

Because all of the angles in the figure are right angles, each
line segment is either horizontal or vertical.

The height of the figure is $3x$ and
the width of the figure is $2x$ .

This means that the length of the unmarked vertical segment must equal
$3x - x = 2x$ .

Also, the length of the unmarked horizontal segment must equal $2x - x = x$ .

Starting in the top left corner and adding lengths in a clockwise
direction, the perimeter is $x + 2x + x + x +
2x + 3x = 10x$.

Alternatively, we can "complete the rectangle" by sliding the shortest
horizontal side and the shortest vertical side as shown to form a
rectangle with height $3x$ and width
$2x$ :

[[IMAGE0]]

The perimeter of this rectangle is $2\times 2x + 2 \times 3x = 10x$ .

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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.