Equations A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 90 yards, what are its dimensions? The width is \( \square \) yards.

To find the dimensions of the athletic field, we can start by letting the width be \( w \) yards. Since the length is twice the width, we express it as \( 2w \) yards. The perimeter (P) of a rectangle is given by the formula \( P = 2(\text{length} + \text{width}) \). Plugging in the values, we have: \[ 90 = 2(2w + w) \] This simplifies to: \[ 90 = 2(3w) \] \[ 90 = 6w \] Dividing both sides by 6 gives: \[ w = 15 \] Thus, the width of the athletic field is 15 yards, and its length is \( 2 \times 15 = 30 \) yards. If you’re ever stuck on a problem like this, remember to clearly define your variables at the start! This not only helps in maintaining clarity but also ensures that you don’t mix up your dimensions later on. Double-checking your perimeter calculation by plugging the numbers back into the formula can also save you from hiccups. For more practice, you might explore resources that feature word problems involving geometry. They can enhance your problem-solving skills while being a fun way to apply mathematical concepts in real situations, like calculating the area for a backyard garden or finding materials for a DIY project!