The perimeter of a rectangle is 128m. The length is 4m more than twice the width.
Find the dimensions.
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To find the dimensions of the rectangle, we need to set up an equation using the given information.
Let's assume the width of the rectangle is "w" meters.
According to the given information, the length of the rectangle is 4 meters more than twice the width, which can be expressed as (2w + 4) meters.
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Substituting the length and width into the formula, we can set up the equation:
128 = 2(2w + 4) + 2w
First, simplify the equation:
128 = 4w + 8 + 2w
Combine like terms:
128 = 6w + 8
Next, isolate the variable:
6w = 128 - 8
6w = 120
Now, divide both sides of the equation by 6:
w = 120/6
w = 20
So, the width of the rectangle is 20 meters.
To find the length, we substitute the value of the width (w) into the expression for the length:
l = 2w + 4 = 2(20) + 4 = 40 + 4 = 44
Therefore, the length of the rectangle is 44 meters.
Thus, the dimensions of the rectangle are:
Width = 20 meters
Length = 44 meters