Rectangles

How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles.

Result

n =  6

Solution:

$S = ab = 60 \ \\ a>b \ \\ 60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5 \ \\ \ \\ a_{ 1 } = 10, b_{ 1 } = 6 \ \\ a_{ 2 } = 12, b_{ 2 } = 5 \ \\ a_{ 3 } = 15, b_{ 3 } = 4 \ \\ a_{ 4 } = 20, b_{ 4 } = 3 \ \\ a_{ 5 } = 30, b_{ 5 } = 2 \ \\ a_{ 6 } = 60, b_{ 6 } = 1 \ \\ \ \\ n = 6$

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