A rectangular room is 3 times as long as it is wide

A rectangular room is 3 times as long as it is wide and its perimeter is 64 meters. Find the dimensions of the room. Define the Width: We start by defining the width of the room as w meters. Why? Because we need a starting point, and the width is a basic dimension of the rectangle. Define the Length: The question states that the room is "3 times as long as it is wide." Therefore, we define the length as 3w meters. Why? Because the length is 3 times the width, as stated in the question. Understand Perimeter: The perimeter of a rectangle is calculated as P = 2 * (length + width). Why? Because that's the formula for the perimeter of a rectangle. Plug in Given Perimeter: We know the perimeter is 64 meters, so we set P to 64. This gives us the equation 64 = 2 * (3w + w). Why? Because we're using the given perimeter to find the dimensions. Combine Like Terms: Inside the parentheses, combine 3w and w to get 4w. Now the equation is 64 = 2 * 4w. Why? Because we're simplifying the equation to make it easier to solve. Distribute the 2: Multiply 2 by 4w to get 8w. The equation becomes 64 = 8w. Why? Because we're simplifying the equation further. Isolate w: To find w, divide both sides of the equation by 8. w = 8 meters. Why? Because we're solving for w, which represents the width. Find the Length: Now that we know w, we can find the length. The length is 3 * 8, which is 24 meters. Why? Because the length is 3 times the width.