Question 194682
I'm not sure how you got what you have, but I think you're confusing the area and perimeter formulas.


Since "A rectangle is 7 times as long as it is wide", this means that {{{L=7W}}}. Also, because "Its area is 1400cm^2", we know that {{{A=1400}}}



Recall, the area of a rectangle is {{{A=LW}}}



{{{A=LW}}} Start with the area of a rectangle formula



{{{1400=7W*W}}} Plug in {{{L=7W}}} and {{{A=1400}}}



{{{1400=7W^2}}} Multiply



{{{1400/7=W^2}}} Divide both sides by 7 



{{{200=W^2}}} Reduce



{{{W^2=200}}} Rearrange the equation



{{{W=sqrt(200)}}} Take the square root of both sides. Note: we're only considering the positive square root.



{{{W=sqrt(100*2)}}} Factor 200 to get 100*2



{{{W=sqrt(100)*sqrt(2)}}} Break up the square root.



{{{W=10*sqrt(2)}}} Take the square root of 100 to get 10



{{{L=7W}}} Go back to the first equation



{{{L=7*10*sqrt(2)}}} Plug in {{{W=10*sqrt(2)}}}



{{{L=70*sqrt(2)}}} Multiply




So the length is {{{70*sqrt(2)}}} cm and the width is {{{10*sqrt(2)}}} cm