SOLUTION: Hi there, I have a question about geometry for homework. My problem is: "A rectangle with a perimeter of 64 inches has one side that is 4 inches shorter than the other. What are t

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Question 171804: Hi there,
I have a question about geometry for homework. My problem is: "A rectangle with a perimeter of 64 inches has one side that is 4 inches shorter than the other. What are the dimensions of the rectangle?"
I don't know how to solve it but this is what I tried:
64 divided by 4 = x
I don't think this is right, please help me.
Thank you!
-Jenn
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length and y=width

Remember, the perimeter formula is P=2L%2B2W where L and W is the length and
width


"A rectangle with a perimeter of 64 inches" translates to 64=2x%2B2y

and

"one side that is 4 inches shorter than the other" translates to y=x-4


64=2x%2B2y Start with the first equation


64=2x%2B2%28x-4%29 Plug in y=x-4


64=2x%2B2x-8 Distribute.


64=4x-8 Combine like terms on the right side.


64%2B8=4x Add 8 to both sides.


72=4x Combine like terms.


72%2F4=x Divide both sides by 4 to isolate x.


18=x Reduce


So the first answer is x=18 which means that the length is 18 inches


------------------------------------------


y=x-4 Go back to the second equation


y=18-4 Plug in x=18


y=14 Subtract


So the second answer is y=14 which means that the width is 14 inches.



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Answer:


So the length is 18 inches and the width is 14 inches