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

Number of solutions found: 6

Calculated by our Diofant problems and integer equations.

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