The length of a new rectangular playing field is 6 yards longer than triple the width. If the perimeter of the rectangular playing 0 of 1 field is 380 yards, what are its dimensions? The width is \( \square \) yards.

Let's take a fun little mathematical journey! The problem states that the length (L) is 6 yards longer than triple the width (W). Mathematically, we can represent this as: \[ L = 3W + 6 \] Now, the perimeter (P) of a rectangle is given by the formula \( P = 2L + 2W \). Since the perimeter is 380 yards, we can express that as: \[ 2L + 2W = 380 \] Now, substitute the expression for L into the perimeter equation: \[ 2(3W + 6) + 2W = 380 \] Solving this will take us to the width. Combine like terms: \[ 6W + 12 + 2W = 380 \] \[ 8W + 12 = 380 \] \[ 8W = 368 \] \[ W = 46 \] Now that we have the width (46 yards), we can easily find the length: \[ L = 3(46) + 6 = 138 \] So, the dimensions of the field are 46 yards in width and 138 yards in length. Have you ever wondered how many sports could be played on such a field? Well, at that size, you'd have plenty of room for soccer, football, or even a practice zone for track and field events! All you need is a bit of imagination and some cones to mark the boundaries! And speaking of playing fields, did you know that rectangular fields are often designed with a specific ratio in mind to enhance gameplay? The proportions can significantly affect the dynamics of the game being played. The ideal dimensions can vary depending on the sport, so it’s always interesting to see how dimensions play a role in the strategies and skills showcased on the field!