Track / Stage 1 / 194 of 320 #194 of 2604

Problem 194

Combinatorics Difficulty 1.3 Multiple choice CEMC Gauss (Grade 8) · Canada · 2020

A bag contains letters as shown.

Elina randomly chooses one of the letters from the bag. What is the probability that Elina chooses a B?

Pick one

Official 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 $x=11$ .

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