The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

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Define variables for the dimensions of the tennis court: let the width be \(w\) feet, and the length be \(l\) feet.

Express the length in terms of the width using the given relationship: \(l = 2w + 6\).

Recall the formula for the perimeter of a rectangle: \(P = 2l + 2w\). Substitute the given perimeter value: \(228 = 2l + 2w\).

Substitute the expression for \(l\) from step 2 into the perimeter equation: \(228 = 2(2w + 6) + 2w\).

Simplify and solve the resulting equation for \(w\), then use the value of \(w\) to find \(l\) using \(l = 2w + 6\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Formulating Algebraic Expressions from Word Problems

This involves translating verbal descriptions into mathematical expressions or equations. For example, 'the length is 6 feet longer than twice the width' can be written as L = 2W + 6, where L is length and W is width.

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around it, calculated as P = 2(L + W), where L is length and W is width. This formula helps relate the dimensions to the given perimeter value.

Solving Linear Equations

Once the problem is expressed as an equation, solving linear equations involves isolating variables to find their values. This includes combining like terms and using inverse operations to solve for unknowns.