46 inches and 27 inches
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Let's denote the length of the rectangle as l and the width as w.
From the problem, we know that the perimeter of a rectangle is calculated as:
Since we are given the perimeter as 146 inches, we can form our first equation:
- 2l + 2w = 146 or
- l + w = 73
The problem states that the width is 4 inches more than one-half of its length.
This gives us our second equation:
Now, we can substitute the value of w from our second equation into our first equation:
Simplifying this equation, we get:
- (3/2)*l + 4 = 73
- (3/2)l = 69
- 3l = 138
- l = 46
Now that we have the length, we can substitute l into the second equation to solve for w:
- w = (1/2)*46 + 4
- w = 23 + 4
- w = 27
So, the dimensions of the rectangle are:
- length = 46 inches
- width = 27 inches