Two rectangles

I cut out two rectangles with 54 cm² and 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.

Correct answer:

n =  6

Step-by-step explanation:

54=ab 90=bc  b = 90/c  54c = 90a 3c = 5a  a=3, b=18, c=5 a=6, b=9, c=10 a=9, b=6, c=15 a=18, b=3, c=30 a=27, b=2, c=45 a=54, b=1, c=90  S = b (a+c)  cm S1=18 8=144 cm2 S2=9 16=144 cm2 S3=6 24=144 cm2 S4=3 48=144 cm2 S5=2 72=144 cm2 S6=1 144=144 cm2  n=6

The equations have the following integer solutions:

Number of solutions found: 6
a1=3, b1=18, c1=5
a2=6, b2=9, c2=10
a3=9, b3=6, c3=15
a4=18, b4=3, c4=30
a5=27, b5=2, c5=45
a6=54, b6=1, c6=90

Calculated by our Diofant problems and integer equations.

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