The length

The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the rectangle's dimensions.

Correct answer:

a =  18 m
b =  12 m

Step-by-step explanation:

$$\begin{gathered} a=2b-6 \\ S=ab \\ S=216{\text{m}}^2 \\ a(a+6)/2=S \\ a(a+6)/2=216 \\ 0.5a^2+3a-216=0 \\ p=0.5;q=3;r=-216 \\ D=q^2-4pr=3^2-4\cdot 0.5\cdot (-216)=441 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{-3\pm \sqrt{441}}{1}=-3\pm 21\sqrt{1} \\ {a}_{1,2}=-3\pm 21 \\ {a}_1=18 \\ {a}_2=-24 \\ a=a_1=18=18\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=(a+6)/2=(18+6)/2=12\text{m}$

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