Question 1012249
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W=width; L=length=W+4cm
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{{{LW+18cm^2=(L+1cm)(W+1cm)}}}
{{{(W+4cm)(W)+18cm^2=(W+5cm)(W+1cm)}}}
{{{W^2+4W+18=W^2+6W+5}}}
{{{4W+18=6W+5}}}
{{{18=2W+5}}}
{{{13=2W)))
{{{6.5=W}}}
ANSWER 1: The width is 6.5 centimeters.
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L=W+4cm=6.5cm+4cm=10.5cm
ANSWER 2: The length is 10.5 centimeters.
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CHECK:
{{{LW+18cm^2=(L+1cm)(W+1cm)}}}
{{{(10.5cm)(6.5cm)+18cm^2=(10.5cm+1cm)(6.5cm+1cm)}}}
{{{68.25cm^2+18cm^2=(11.5cm)(7.5cm)}}}
{{{86.25cm^2=86.25cm^2}}}