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Chapter 2: Problem 35

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.

Short Answer

Expert verified
The width of the field is 160 feet and the length is 360 feet.

Step by step solution

01

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.
02

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 \(1040 = 2 * (x + (x + 200))\).
03

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 \(x\).
04

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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