Final answer:
To calculate the width of a rectangle when given the area and length, divide the area by the length. In this case, width is found by simplifying the expression (x² - 4) / ((x+2)²).
Step-by-step explanation:
To find the width of the rectangle with an area of x² - 4 / 2x in² and a length of (x+2)² /2 in, we need to apply the formula for the area of a rectangle, which is Area = Length × Width. Since we have the area and the length, we can divide the area by the length to get the width.
The area given is x² - 4 / 2x, and the length is (x+2)² / 2. To find the width, we divide the area by the length:
Width = Area / Length
Plugging in the given values:
Width = (x² - 4) / (2x) ÷ 2 / (x+2)²
To simplify this expression, we multiply by the reciprocal of the length:
Width = (x² - 4) / (2x) × 1 / ((x+2)² / 2)
Now, we simplify:
Width = (x² - 4) / ((x+2)²)
Note:
If (x+2)² equals x² - 4, the width would be 1 in. However, for other values of x, further simplification or factoring may be necessary to find the exact width.