SOLUTION: The perimeter of a rectangle is 46 M. The width of the rectangle is two more than half the length. Find a length and width. show your solution

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Question 1059379: The perimeter of a rectangle is 46 M. The width of the rectangle is two more than half the length. Find a length and width. show your solution
Answer by acw1213(28) About Me  (Show Source):
You can put this solution on YOUR website!
We need to write a system of equations here.
Let "L" represent the length.
Let "w" represent the width.
Let "p" represent the perimeter.
The formula for the perimeter of a rectangle is
2L + 2w = p
Plug in 46 for "p" since this our perimeter.
2L + 2w = 46
Yay! We are done with one equation!
Now write the other equation.
The width is equal to TWO more than HALF OF THE LENGTH. Show this in an equation format!
1/2L + 2 = w

We have our systems as of now. Let's solve for the length and width.
As you can see, we can substitute 1/2L + 2 for "w" in the first equation.
2L + 2(1/2L + 2) = 46 Distribute the 2
2L + L + 4 = 46 Combine like terms
3L + 4 = 46 Subtract 4 on both sides
3L = 42 Divide by 3
L = 14
Our length is 14 m., now let's plug in 14 for "L" in the second equation.
1/2(14) + 2 = w
7 + 2 = w
w = 9
Our width is 9 m.
Our length is 14 m.