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To solve linear equations, follow a step-by-step approach. This means breaking down the problem into manageable pieces and tackling each part one by one.
Start by identifying the variables involved. For instance, in our example, the length (L) and width (W) are the variables. Then, set up relationships between these variables using the information from the problem.
In our exercise, the width (W) is 42 feet less than the length (L), which gives us the equation:
W = L - 42.
Next, use any other provided information to create another equation. Here, we know the perimeter (P) of the rectangle is 228 feet. The formula for the perimeter is:
P = 2L + 2W.
Substitute the first equation into this formula to get a single equation in one variable. This will typically involve some simplification steps.
Finally, solve the simplified equation for the variable. In this case, solving for L first, then using it to find W. Always verify your solution by substituting the values back into the original equations.

Understanding the perimeter formula is crucial when dealing with geometric problems. The perimeter of a rectangle is the sum of all its sides.
The formula is given by:
P = 2L + 2W
where P is the perimeter, L is the length, and W is the width.
In our example, the perimeter is provided as 228 feet. We know the length (L) and width (W) relationship from the problem statement. By substituting appropriate values and simplifying, we can solve for both dimensions of the rectangle.
To reinforce understanding, consider different shapes or contexts: For example, a square has all sides equal, so its perimeter formula would be P = 4s, where s is the side length. But for a rectangle, always use P = 2L + 2W.

Finding the dimensions of a rectangle often involves solving for its length (L) and width (W).
In real-world problems, certain relationships or constraints are usually provided, like in our tennis court example, where the width is 42 feet less than the length.
Step-by-step:

• Identify relationships: W = L - 42.
• Use the perimeter formula: P = 2L + 2W.
• Substitute and simplify: 228 = 2L + 2(L - 42).

Solving for L, we find L = 78 feet.
Substitute back to find W: W = 78 - 42, giving W = 36 feet.
Always verify by recalculating the perimeter to ensure it matches the provided value. This thorough approach ensures accurate results and reinforces understanding.