Let's define the variables:

• Let $L$ be the length of the rectangle.
• Let $W$ be the width of the rectangle.

Step 1: Express Width in Terms of Length

Since the width is 9 cm shorter than the length:
$W = L - 9$

Step 2: Use the Perimeter Formula

The perimeter of a rectangle is given by:
$P = 2L + 2W$

Substituting $P = 102$ and $W = L - 9$:
$2L + 2(L - 9) = 102$

Step 3: Solve for $L$

$2L + 2L - 18 = 102$ $4L - 18 = 102$ $4L = 120$ $L = 30$

Step 4: Identify the Correct Equation

Looking at the answer choices, the correct equation should match:
$L + L - 9 + L + L - 9 = 102$ which simplifies to:
$4L - 18 = 102$

Thus, the correct answer choice is:
"L + L - 9 + L + L - 9 = 102; L = 30 cm"

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Would you like further clarification?

Related Questions:

1. What is the width of the rectangle?
2. How do you derive the equation for perimeter in general?
3. How would the equation change if the width were 12 cm shorter instead?
4. What would be the length if the perimeter were 120 cm instead?
5. How do you verify that the calculated length is correct?

Tip:

Always check your final answer by plugging it back into the original equation!