Question 188378
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P=2L+2W= 200cm, eqn1
A=L*W= 2491 sq.cm., eqn2


In eqn 2 we get, {{{L*cross(W)/cross(W)=2491/W}}} ---> L=2491/W, eqn3


Substitute eqn 3 in eqn 1:
{{{2((highlight(2491/W)))+2W=200}}}
{{{4982/W+2W=200}}} ---> {{{(4982+2W^2)/W=200}}}, cross multiply
{{{2W^2+4982=200W}}} ---> {{{2W^2+4982-200W=0}}}, divide whole eqn by 2:
{{{W^2-100W+2491=0}}}
By Quadratic, where{{{system(a=1,b=(-100),c=2491)}}}
Discriminant: {{{b^2-4ac=100^2-4(1)(2491)=10000-9961=red(36)}}}
Then,
{{{x=(-(100)+-sqrt(36))/(2*1)=100+-6/2}}}
{{{x=100+6/2=106/2=red(53)}}}
{{{x=100-6/2=94/2=red(47)}}}
For Width you got 2 values, <font color=blue>W1=53cm; W2=47cm</font>


For Length: Via eqn 3,
{{{L[1]=2491/W[1]=2491/53=red(47cm)}}}, and {{{L[2]=2491/W[2]=2491/47=red(53cm)}}}
<font color=blue>L1=47cm; L2=53cm</font>


Check on Perimeter:
{{{200cm=2(L[1])+2(W[1])}}}
{{{200cm=2(47)+2(53)}}}
{{{200cm=94cm+106cm}}}
{{{200cm=200cm}}}
We use L2 & W2 on Area:
{{{2491cm^2=47*53}}}
{{{2491cm^2=2491cm^2}}}


Therefore, Rectangle can be of <font color=blue>L1 & W1 or L2 & W2</font>


Thank you,
Jojo</font>