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rectangles of equal area, and sides in arithmetic progression

Source: Mexico National Olympiad 2021 Problem 1

November 10, 2021
arithmetic sequencerectanglealgebra

Problem Statement

The real positive numbers a1,a2,a3a_1, a_2,a_3 are three consecutive terms of an arithmetic progression, and similarly, b1,b2,b3b_1, b_2, b_3 are distinct real positive numbers and consecutive terms of an arithmetic progression. Is it possible to use three segments of lengths a1,a2,a3a_1, a_2, a_3 as bases, and other three segments of lengths b1,b2,b3b_1, b_2, b_3 as altitudes, to construct three rectangles of equal area ?
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