Rectangle

The perimeter of the rectangle is 22 cm and content area 30 cm^2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.

Result

a =  5 cm
b =  6 cm

Solution:

a=1; b=11-a=10; S = ab=10
a=2; b=11-a=9; S = ab=18
a=3; b=11-a=8; S = ab=24
a=4; b=11-a=7; S = ab=28
a=5; b=11-a=6; S = ab=30 <<<<<< OK
a=6; b=11-a=5; S = ab=30 <<<<<< OK
a=7; b=11-a=4; S = ab=28
a=8; b=11-a=3; S = ab=24
a=9; b=11-a=2; S = ab=18
a=10; b=11-a=1; S = ab=10

The equations have the following integer solutions:

2(a+b)=22
ab = 30

a=5, b=6
a=6, b=5

Number of solutions found: 2

Calculated by our Diofant problems and integer equations.

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