Rectangle

The perimeter of the rectangle is 22 cm and content area 30 cm2. 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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