Question 147955
Let x=length and y=width


Remember, the perimeter formula is {{{P=2x+2y}}}. Since the perimeter is 66 inches, this means that {{{P=66}}}. So the equation is now {{{66=2x+2y}}}. 



Also, because the "length exceeds the width by 27 inches", this tells us that {{{x=y+27}}}



{{{66=2x+2y}}} Start with the first equation.



{{{66=2(y+27)+2y}}} Plug in {{{x=y+27}}}



{{{66=2y+54+2y}}} Distribute.



{{{66=4y+54}}} Combine like terms on the right side.



{{{0=4y+54-66}}} Subtract {{{66}}} from both sides.



{{{-4y=54-66}}} Subtract {{{4y}}} from both sides.



{{{-4y=-12}}} Combine like terms on the right side.



{{{y=(-12)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{y}}}.



{{{y=3}}} Reduce.


So the width is 3 inches. 



{{{x=y+27}}} Go back to the second equation.



{{{x=3+27}}} Plug in {{{y=3}}}



{{{x=30}}} Add.



So the length is 30 inches



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Answer:



So the length is 30 inches and the width is 3 inches