# How many

How many different rectangles with integer page lengths have an area S = 60 cm²?

Correct 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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