Rectangles

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

Correct result:

n =  6

Solution:

S=ab=60 a>b 60=2×2×3×5=22×3×5  a1=10,b1=6 a2=12,b2=5 a3=15,b3=4 a4=20,b4=3 a5=30,b5=2 a6=60,b6=1  n=6S=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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