Rectangle

The perimeter of the rectangle is 22 cm, and the area is 30 cm2. Determine its dimensions if integers express the length of the sides of the rectangle in centimeters.

Correct answer:

a =  5 cm
b =  6 cm

Step-by-step explanation:


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


Number of solutions found: 2
a1=5, b1=6
a2=6, b2=5

Calculated by our Diofant problems and integer equations.



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