Number theory · Divisibility · Greatest common divisor · Rectangle dissection · Optimisation
A large rectangle is cut into seven smaller rectangles, each of which has both of its side lengths equal to a whole number of metres. Five of the seven pieces have their areas written in them, as shown below. What is the smallest possible total area, in square metres, of the remaining two pieces?
- A \(36\)
- B \(54\)
- C \(64\)
- D \(76\)
- E \(81\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2022, 1. letnik, category A, problem A2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source