SOLUTION: 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. it is Deb again with a word pro

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Question 101955: 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.
it is Deb again with a word problem please help.
Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
Ok first lets define perimeter of a rectangle.
The perimeter of a rectangle is equal to the sum of all its sides.
A rectangle has four sides.
The two sides that make up its length are equal to each other.
And the two sides that make up its width are equal to each other.
So since we have two sides that are length
and two sids that are width. We know that
2 times the length plus two times the width equals the perimeter.
Write this sentence as an equation.
2L + 2W = P
Now lets look at the rectangle in our problem.
Lets set the width equal to x
width = x
Ok now we are told that:
The length of a rectangle is 2 in. more than twice its width.
So if width = x then,
length = 2x + 2
The problem also tells us that the perimeter is 34 in
Now lets put all of this information into the equation for perimeter.
2L + 2W = P
2(2x+2) + 2x = 34
Now we have an equation with one variable to solve for. Lets do it.
2(2x+2) + 2x = 34
distribute the 2 across (2x+2)
to do this multiply 2 times 2x and 2 times 2
4x + 4 + 2x = 34
now combine like terms 4x + 2x
6x + 4 =34
move 4 to other side of the equation by subtracting it from both sides
6x + 4 - 4 = 34 -4
6x = 30
finally divide both sides by 6 to solve the equation
6x/6 = 30/6
x = 5
Answer: The width is 5 inches
Now use this back in the original equation to find the length.
2L + 2W = P
we know the perimeter is 34 so....
2L + 2W = 34
and we found the width to be 5 so....
2L + 2(5) = 34
now solve for Length
2L + 2(5) = 34
multiply 2 times 5
2L + 10 = 34
move 10 to other side of the equation by subtracting it from both sides
2L + 10 - 10 = 34 - 10
2L = 24
and divide both sides by 2 to solve for L
2L/2 = 24/2
L = 12
Answer: Length is 12 inches
Check answers using the formula for perimeter
2L + 2W = P
2(12) + 2(5) = 34
24 + 10 = 34
34 = 34