Question 203129
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Basic Eqn --> {{{A[R]=L*W}}}


Given: {{{system(Width=x,Length=2x-1,A[R]=120m^2)}}}



Subst.
{{{120m^2=(2x-1)(x)}}}
{{{120m^2=2x^2-x}}}
{{{2x^2-x-120=0}}}, remember{{{system(a=2,b=-1,c=-120)}}}


By Quadratic:
For discriminant, {{{b^2-4ac=-1^2-4(2)(-120)=1+960=961}}}
Therefore,
{{{x=(-(-1)+-sqrt(961))/(2*2)=(1+-31)/4}}}
{{{x=(1+31)/4=32/4=red(8m)}}}
{{{x=(1-31)/4=-30/4=-7.5}}}, disregard, (-)


So, the <font color=blue>Width=x=8meters</font>


Also, the {{{L=2(8)-1=16-1}}}
<font color=blue>Length=15meters</font>


Checking,
{{{A[R]=L*W}}}
{{{120^m2=(15m)(8m)}}}
{{{120m^2=120m^2}}}


Thank you,
Jojo</font>