SOLUTION: Geometry. The length of a rectangle is 2 in. more than twice its width. If the perimeter of the rectangle is 34 in., find the dimensions of the rectangle.

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Question 126270: Geometry. The length of a rectangle is 2 in. more than twice its width. If the
perimeter of the rectangle is 34 in., find the dimensions of the rectangle.
Answer by JessicaGill(40) About Me  (Show Source):
You can put this solution on YOUR website!
Let us begin by assigning variables to the length and height of the rectangle, it is also called base and height, so as long as you are assigning the correct variable to the correct side you should be ok. Remember if taking a test, use the notation P=2b%2B2h
Perimeter equals 2 times the base plus 2 times the height.
1. Let the width be W and the Lenght be L.
2. The formula for a perimiter of a rectangle is P=2l+2w (2 times the lenght plus 2 times the width)
3. In this problem the length is 2 inches greater than 2 times the width so let us set L to %282%2Aw%29%2B2 and W will remain the same.
4. Now let us plug these values into our formula.
34=2%2A%28%282%2Aw%29%2B2%29%2B2%2Aw
5. Now all that is left is to solve for W. We solve this just like any single variable equation. We need to isolate the W to one side of the equation.
Remember the order of operations when doing problems.
34=2%2A%28%282%2Aw%29%2B2%29%2B2%2Aw
First let us use the distributive property of multiplication. We need to multiply %282%2Aw%29%2B2 by 2.
This gives us 4w%2B4%29
So now our formula looks like this 34=4w%2B4%2B2w or to simplfy 34=6w%2B4
Now we need to subtract 4 from each side of the equation
34-4=6w%2B4-4
Which gives us 30=6w
Now divide each side of the equation by 6
30%2F6=6w%2F6
This leaves us with 5=w
Now we have determined that the W or width of our rectangle is 5. The next step is to check our work by plugging in 5 for the w in our perimeter equation.
34=2%2A%282w%2B2%29%2B2w
34=%282%2A%282%2A5%29%2B2%29%2B2%2A5 replacing w with 5
34=%282%2A%2810%29%2B4%29%2B10 following order of operations, multiplication
34=20%2B4%2B10 addition
34=34 result
So our width is 5, now to figure our length with is %282%2A5%29%2B2 or 10%2B2 which simplifies to 12.
Answers Width 5 Length 12
Simple check 34=2%2A5%2B2%2A12
34=10%2B24
34=34