Glass panel

A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?

Result

a =  24 cm
n =  12

Solution:

$72 = 2^3 \cdot 3^2 \\ 96 = 2^5 \cdot 3 \\ \text{GCD}(72, 96) = 2^3 \cdot 3 = 24\\ \ \\ \ \\ a = GCD(72,96) = 24 = 24 \ \text{ cm }$

$S = 72 \cdot \ 96 = 6912 \ cm^2 \ \\ S_{ 2 } = a^2 = 24^2 = 576 \ cm^2 \ \\ n = S/S_{ 2 } = 6912/576 = 12$

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