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.

Final Answer:

a =  5 cm
b =  6 cm

Step-by-step explanation:

$$\begin{gathered} 2(a+b)=22\text{cm} \\ ab=30{\text{cm}}^2 \\ a(11-a)=30 \\ -a^2+11a-30=0 \\ {a}^2-11a+30=0 \\ p=1;q=-11;r=30 \\ D=q^2-4pr=11^2-4\cdot 1\cdot 30=1 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{11\pm \sqrt{1}}{2} \\ {a}_{1,2}=\frac{11\pm 1}{2} \\ {a}_{1,2}=5.5\pm 0.5 \\ {a}_1=6 \\ {a}_2=5 \\ a=5=5\text{cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=6=6\text{cm}$

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