To find the perimeter of a rectangle, you can use the formula:
\[ P = 2 \times (length + width) \]
In this case, the given perimeter \( P \) is 32 inches, the width is 4 inches, and the length is given as \( 2.5x \) inches.
Substituting the values into the perimeter formula, we get:
\[ 32 = 2 \times (2.5x + 4) \]
To simplify this equation, first divide both sides by 2:
\[ 16 = 2.5x + 4 \]
Now, subtract 4 from both sides:
\[ 12 = 2.5x \]
We can re-organize this into a different format to find a suitable option. To do that, we can convert this equation into a comparison of widths and lengths.
The total width in terms of its component form, because there are two widths (4 inches each), is:
\[ 8 \]
And the total length in terms of its component form twice length (2.5x) is:
\[ 5x \]
Putting both sides together gives:
\[ 8 + 5x = 32 \]
Now, looking at the options:
A) \( 4 + 2.5x = 32 \)
B) \( 8 + 5x = 32 \)
C) \( 4(2.5x) = 32 \)
D) \( 8(5x) = 32 \)
The correct option is:
B. \( 8 + 5x = 32 \)