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.

Result

a =  18 m
b =  12 m

Solution:

$a=2b -6 \ \\ S=ab=216 \ \\ \ \\ a(a+6)/2=216 \ \\ \ \\ 0.5a^2 +3a -216=0 \ \\ \ \\ p=0.5; q=3; r=-216 \ \\ D=q^2 - 4pr=3^2 - 4\cdot 0.5 \cdot (-216)=441 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ -3 \pm \sqrt{ 441 } }{ 1 }=-3 \pm 21 \sqrt{ 1 } \ \\ a_{1,2}=-3 \pm 21 \ \\ a_{1}=18 \ \\ a_{2}=-24 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 0.5 (a -18) (a +24)=0 \ \\ \ \\ a=a_{1}=18 \ \text{m}$

Checkout calculation with our calculator of quadratic equations.

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

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