The length of a rectangle is two more than three times its width. The perimeter of the rectangle is 116. Determine the length and width of the rectangle.

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To determine the length and width of the rectangle, we can set up an equation based on the given information. Let's denote the width of the rectangle as 'w' and the length as 'l'.

Given that the length of the rectangle is two more than three times its width, we can write the equation:
l = 3w + 2

The perimeter of a rectangle is found by adding the lengths of all its sides. In this case, the perimeter is given as 116. For a rectangle, this can be represented as:
P = 2(l + w)

Substituting the value of l from the first equation into the perimeter equation, we have:
116 = 2((3w + 2) + w)

Now we can solve for w. First, distribute the 2 to both terms inside the bracket:
116 = 2(3w + 2) + 2w

Simplify by multiplying the 2 to the terms inside the bracket:
116 = 6w + 4 + 2w

Combine like terms:
116 = 8w + 4

Next, isolate the variable by subtracting 4 from both sides:
116 - 4 = 8w
112 = 8w

Then, divide both sides by 8 to solve for w:
w = 112 / 8
w = 14

The width of the rectangle is 14.

Now, to find the length (l), substitute the value of w back into the equation for l:
l = 3w + 2
l = 3(14) + 2
l = 42 + 2
l = 44

The length of the rectangle is 44.

Therefore, the length of the rectangle is 44 units and the width is 14 units.

L = 3W +2

2L + 2W = 116

Substitute 3W+2 for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.