Circumference 6040

The picture shows a square net in which the side of one square is 1 cm long. Draw a rectangle with an area of 18 squares with a circumference of 22 cm.

Correct answer:

a =  9 cm
b =  2 cm

Step-by-step explanation:

$$\begin{gathered} S=ab=18{\text{cm}}^2 \\ o=2a+2b=22\text{cm} \\ b=(22-2a)/2 \\ a\cdot (22-2\cdot a)/2=18 \\ a\cdot (22-2\cdot a)/2=18 \\ -a^2+11a-18=0 \\ {a}^2-11a+18=0 \\ p=1;q=-11;r=18 \\ D=q^2-4pr=11^2-4\cdot 1\cdot 18=49 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{11\pm \sqrt{49}}{2} \\ {a}_{1,2}=\frac{11\pm 7}{2} \\ {a}_{1,2}=5.5\pm 3.5 \\ {a}_1=9 \\ {a}_2=2 \\ a=a_1=9=9\text{cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=(22-2a)/2=(22-2\cdot 9)/2=2\text{cm}$

Try another example