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

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) (Show Source): You can put this solution on YOUR website!
Let L=length of the rectangle, w=width of the rectangle, = perimeter of the square, and = perimeter of the rectangle

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

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

"the width of the rectangle is 2m less than the side of the square

And this is what we know :
Perimeter of the square:

Perimeter of the rectangle

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

since , we can substitute that into .

Plug in

Multiply

Since and , set them equal to each other

Now plug in and

Distribute

Combine like terms on the right side

Add 24 to both sides

Subtract 4S from both sides

Combine like terms on the left side

Combine like terms on the right side

Divide both sides by 4 to isolate S

Divide

--------------------------------------------------------------
Answer:
So our answer is

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

So the length is 11m

This also means the width of the rectangle is:

So the width is 5m

Check:

First find the perimeter of the square:

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

Now find the perimeter of the rectangle

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