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, 2020

Geometry Difficulty 2.3 Junior Find the answer Canada

In the diagram, the perimeter of the triangle is equal to the perimeter of the rectangle.

What is the value of $x$ ?

Pick one

Solution

The triangle is isosceles, and so the missing side length is also 12 cm.

The perimeter of the triangle is $14+12+12=38$ cm.

The perimeter of the rectangle is given by $x+8+x+8=2x+16$ cm.

The perimeter of the triangle is equal to the perimeter of the rectangle, and so $2x+16=38$ .
Since $22+16=38$ , then $2x=22$ and so $x=11$ .

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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.