Problem 25 - Algebra and Trigonometry

Question

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?

Step-by-Step Solution

Answer

The dimensions of the soccer field are 50 yards wide and 100 yards long.

Step 1: Understanding the problem

The problem states that a soccer field is rectangular, its length is twice as wide, and the sum of all sides (perimeter) is 300 yards. Therefore, we know that the length of the field is \(2x\) and its width is \(x\), and that the sum of both (multiplied by 2) should be equal to 300: \(2(2x + x) = 300\). The main objective is to find the values of \(x\) (width) and \(2x\) (length).

Step 2: Set up the equation

From what's given, we can set up the equation as: \(2(2x + x) = 300\). This is the equation representing the perimeter, based on the given information.

Step 3: Simplify the equation

First, simplify inside the brackets: \(2(3x) = 300\). This results in \(6x = 300\).

Step 4: Solve the equation

To find the value of \(x\), divide both sides of the equation by 6: \(x = 300 / 6\). That gives \(x = 50\). This is the width of the soccer field.

Step 5: Find the length

According to the problem, the length of the soccer field is twice the width, so we just need to multiply the width \(x\) by 2. Therefore, the length is \(2 * 50 = 100\) yards.