Problem 35
Question
An American football field is a rectangle with a perimeter of 1040 feet. The length is 200 feet more than the width. Find the width and length of the rectangular field.
Step-by-Step Solution
Verified Answer
The width of the field is 160 feet and the length is 360 feet.
1Step 1: Define the Variables
Let's define \(x\) as the width of the rectangular field. Then, the length of the field can be represented as \(x + 200\), given that it is 200 feet more than the width.
2Step 2: Establish the Perimeter Formula
The formula for the perimeter of a rectangle is given by \(P = 2*(length + width)\). Substituting the defined variables into the formula, we obtain a relationship \(1040 = 2 * (x + (x + 200))\).
3Step 3: Solve the Equation
Now solve this equation for \(x\). Begin by expanding the equation to get \(1040 = 2*(2x + 200)\), which simplifies to \(1040 = 4x + 400\). Then, subtract 400 from both sides to isolate the expression for \(x\), which gives \(640 = 4x\). Finally, divide both sides by 4 to solve for \(x\).
4Step 4: Calculate the Length
Once you have the width (\(x\)), the length can be calculated by adding 200 to the width, as per the problem statement.
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