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Problem 253

Geometry Difficulty 1.4 Multiple choice CEMC Cayley · Canada · 2023

A 6 m by 8 m rectangular field has a fence around it. There is a
post at each of the four corners of the field. Starting at each corner,
there is a post every 2 m along each side of the fence. How many posts
are there?

Pick one

Official solution

A rectangle that is 6 m by 8 m has perimeter $2 \times(6\text{ m} + 8\text{ m}) = 28\text{ m}$ .

If posts are put in every 2 m around the perimeter starting at a corner,
then we would guess that it will take $\dfrac{28\text{ m}}{2\text{ m}} = 14$
posts.

The diagram below confirms this:

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