Two rectangles

I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calculation.

Result

n =  6

Solution:

The equations have the following integer solutions:
54=ab
90=bc

a1=-6, b1=-9, c1=-10a2=3, b2=18, c2=5a3=6, b3=9, c3=10a4=9, b4=6, c4=15a5=18, b5=3, c5=30a6=27, b6=2, c6=45a7=54, b7=1, c7=90

Number of solutions found: 7

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