Question 210150
The perimeter P of any rectangle with length L and width W is {{{P=2L+2W}}}. Since the rectangle has "a perimeter of 24", this means {{{P=24}}}. Plug this in to get {{{24=2L+2W}}}. This is our first equation.


Also, since "the Length is 3 inches greater then the width", this means that we take the unknown width W and add 3 inches to it to get the length L. Algebraically, we get: {{{L=W+3}}}



{{{24=2L+2W}}} Start with the first equation.



{{{24=2(W+3)+2W}}} Plug in {{{L=W+3}}}



{{{24=2W+6+2W}}} Distribute.



{{{24=4W+6}}} Combine like terms.



{{{24-6=4W}}}  Subtract {{{6}}} from both sides.



{{{18=4W}}} Combine like terms.



{{{(18)/4=W}}} Divide both sides by {{{4}}} to isolate {{{W}}}.



{{{9/2=W}}} Reduce.



{{{W=9/2}}} Rearrange the equation.



{{{W=4.5}}} Divide



So the width is 4.5 inches.



Since the length is "3 inches greater then the width", just add 3 to the width to get the length like so: {{{L=4.5+3=7.5}}}



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Answer:



So the length and width are 7.5 inches and 4.5 inches respectively.