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 dimensions of the rectangle.

Correct answer:

a =  18 m
b =  12 m

Step-by-step explanation:

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

Our quadratic equation calculator calculates it.

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

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