A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

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Let the width of the soccer field be represented by $w$ yards.

Since the length is twice the width, express the length as \$2w$ yards.

Recall the formula for the perimeter of a rectangle: $P = 2 \times (\text{length} + \text{width})$.

Substitute the given perimeter and expressions for length and width into the formula: $300 = 2 \times (2w + w)$.

Simplify the equation and solve for $w$, then use the value of $w$ to find the length \$2w$.

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주요 개념

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

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around it, calculated by adding twice the length and twice the width (P = 2L + 2W). Understanding this formula is essential to relate the given perimeter to the dimensions of the soccer field.

Algebraic Representation of Relationships

Translating the problem's conditions into algebraic expressions is crucial. Here, the length is twice the width, so L = 2W. This relationship allows substitution into the perimeter formula to form an equation with one variable.

Solving Linear Equations

Once the equation is set up, solving for the unknown variable involves combining like terms and isolating the variable. This step yields the width, which can then be used to find the length, providing the field's dimensions.