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First, we set up two equations based on the information you have given.
L = 2w + 3
2L + 2W = 18
Now, we use the value for L in the first equation and substitute it into the second equation.
2 (2W + 3) + 2W = 18
4W + 6 + 2W = 18
6W = 12
W = 2
Now we use this value for W to determine L.
L = 2*2 + 3
L = 4 + 3
L = 7
So, the length is 7 inches and the width is 2 inches.
The length of a rectangle is 3 inch more than twice its width.
Let the width of the rectangle be W. The length of the rectangle is 3 + 2*W
For a rectangle with sides W and L the perimeter is equal to 2*(W + L)
Substituting the values in the formula, the perimeter is:
2*(W + 3 + 2*W). This is equal to 18
2*(W + 3 + 2*W) = 18
W + 3 + 2*W = 9
3W + 3 = 9
W = 2
The width of the rectangle is 2 inches.
We'll put the length of the rectangle to be a inches and the width be b inches.
We know, from enunciation, that the length is 3 inches more than twice its width and we'll write the constraint mathematically:
a - 3 = 2b
We'll subtract 2b and add 3 both sides:
a - 2b = 3 (1)
The perimeter of the rectangle is 18 inches.
We'll write the perimeter of the rectangle:
P = 2(a+b)
18 = 2(a+b)
We'll divide by 2:
9 = a + b
We'll use the symmetric property:
a + b = 9 (2)
We'll add (1) + 2*(2):
a - 2b + 2a + 2b = 3 + 18
We'l eliminate and combine like terms:
3a = 21
We'll divide by 3:
a = 7 inches
7 + b = 9
b = 9 - 7
b = 2 inches
So, the length of the rectangle is of 7 inches and the width of the rectangle is of 2 inches.
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