SOLUTION: a rectangle with a perimeter of 34cm has a length that is 3cm more than twice its width. What are the dimensions of the rectangle? Show a complete solution,including "let" and "th

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Question 389447: a rectangle with a perimeter of 34cm has a length that is 3cm more than twice its width. What are the dimensions of the rectangle? Show a complete solution,including "let" and "therefore" statements.
Found 2 solutions by richard1234, gwendolyn:
Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website!
Let the width be w, and the length be 2w + 3. The perimeter is

2(w + (2w+3)) = 34

2(3w + 3) = 34

3w + 3 = 17

w = 14/3, 2w + 3 = 37/3

Answer by gwendolyn(128) (Show Source):
You can put this solution on YOUR website!
Let W be the width of the rectangle.
Let L be the length of the rectangle.
The length is 3 cm more than twice its width. Therefore:
L = 2W + 3
The perimeter of the rectangle is 34 cm. Therefore:
2W + 2L = 34
We can substitute the value of L from the first equation into the second:
2W + 2(2W + 3) = 34
Distributing the 2 on the right:
2W + 2*2W + 2*3 = 34
2W + 4W + 6 = 34
6W + 6 = 34
Subtracting 6 from both sides:
6W + 6 - 6 = 34 - 6
6W = 28
Dividing both sides by 6:

or,
W = 4 and 2/3
We can substitute this value of W back into the first equation
to find the value of L:
L = 2*W + 3

or,
L = 9 and 1/3 + 3 so,
L = 12 and 1/3