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Problem 551

Geometry Difficulty 2.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2015

There is a square whose perimeter is the same as the perimeter of the triangle shown.

The area of that square is

Pick one

Official solution

The total value of one quarter, one dime and one nickel is $25+10+5=40$ ¢.

Since you have equal numbers of quarters, dimes and nickels, you can separate your coins into piles, each containing exactly 1 quarter, 1 dime, and 1 nickel.

Each pile has a value of 40¢, and since $440\div40=11$ , then you must have 11 quarters, 11 dimes and 11 nickels.

Therefore, you have 11 dimes.
Note: You can check that $11\times(25$ ¢ $\,+ 10$ ¢ $\,+5$ ¢ $)=11\times40$ ¢ $=440$ ¢ $=\$4.40$ , as required.

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