Library / CEMC Gauss (Grade 8) /270 of 525

CEMC Gauss (Grade 8), 2014

Geometry Difficulty 1.3 Junior Find the answer Canada

The perimeter of the isosceles triangle shown is 53 cm.

The value of $x$ is

Pick one

Solution

Solution 1

Evaluating the left side of the equation, we get $9210-9124=86$ .

Therefore the right side of the equation, $210-\Box$ , must also equal 86.
Since $210-124=86$ , then the value represented by the $\Box$ is 124.

Solution 2

Since $9210-9124=(9000+210)-(9000+124)=9000-9000+210-124=210-124$ , then the value represented by the $\Box$ is 124.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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