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Problem 152

Geometry Difficulty 1.2 Find the answer CEMC Pascal · Canada · 2020

In the diagram, $\triangle PQR$ has side lengths as shown.If $x = 10$ , the perimeter of $\triangle PQR$ is $29$ $31$ $25$ $27$ $23$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Solution 1

Since the side lengths of the triangle are $x-1$ , $x+1$ and 7, its perimeter is $(x-1)+(x+1)+7$ which equals $2x+7$ . Since $x=10$ , the perimeter equals $2\times 10 + 7$ which is equal to 27. Solution 2 Since $x=10$ , the side lengths of the triangle are $x-1=9$ and $x+1=11$ and 7. The perimeter of the triangle is thus $9+11+7$ which equals 27.

Figure for this problem

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