SOLUTION: Word problem: The side of a square has length S. The length of a rectangle is 4m more than the side of the square and the width of the rectangle is 2m less than the side of the squ

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Question 103990: Word problem: The side of a square has length S. The length of a rectangle is 4m more than the side of the square and the width of the rectangle is 2m less than the side of the square. The perimeter of the rectangle is 24m less than twice the perimeter of the square. Find the dimension of each figure.

Please help...no idea where to begin.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let L=length of the rectangle, w=width of the rectangle, P%5Bs%5D= perimeter of the square, and P%5Br%5D= perimeter of the rectangle


Let's start with what we know and what we are given


This is what we are given:
L=4%2BS "The length of a rectangle is 4m more than the side of the square"

W=S-2 "the width of the rectangle is 2m less than the side of the square



And this is what we know :
Perimeter of the square:
P%5Bs%5D=4S
Perimeter of the rectangle
P%5Br%5D=2L%2B2W


Remember, the problem says: "The perimeter of the rectangle is 24m less than twice the perimeter of the square". So this means the perimeter of the rectangle is


P%5Br%5D=2P%5Bs%5D-24

since P%5Bs%5D=4S, we can substitute that into P%5Br%5D=2P%5Bs%5D-24.



P%5Br%5D=2%284S%29-24 Plug in P%5Bs%5D=4S


P%5Br%5D=8S-24 Multiply


Since P%5Br%5D=8S-24 and P%5Br%5D=2L%2B2W, set them equal to each other

8S-24=2L%2B2W

8S-24=2%284%2BS%29%2B2%28S-2%29 Now plug in L=4%2BS and W=S-2


8S-24=8%2B2S%2B2S-4 Distribute




8S-24=4S%2B4 Combine like terms on the right side


8S=4S%2B4%2B24Add 24 to both sides


8S-4S=4%2B24 Subtract 4S from both sides


4S=4%2B24 Combine like terms on the left side


4S=28 Combine like terms on the right side


S=%2828%29%2F%284%29 Divide both sides by 4 to isolate S



S=7 Divide

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Answer:
So our answer is S=7



So the side length of the square is 7m. This means the length of the rectangle is:

L=4%2BS=4%2B7=11

So the length is 11m


This also means the width of the rectangle is:

W=S-2=7-2=5

So the width is 5m



Check:

First find the perimeter of the square:
P=4S=4%287%29=28

Now multiply 28 by 2 and subtract 24 to get...

28%2A2-24=32

Now find the perimeter of the rectangle

P=2L%2B2W=2%2811%29%2B2%285%29=22%2B10=32

Since the perimeter of the rectangle is 24 less than twice the perimeter of the square, our answer is verified