The length of a rectangle is six times its width. If the perimeter of the rectangle is 126 yd , find its length and width. width: \( \square \mathrm{yd} \)

To tackle this problem, we can start by letting the width of the rectangle be \( w \) yards. According to the information provided, the length will be \( 6w \) yards. The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2(\text{length} + \text{width}) \] Substituting our expressions for length and width into the formula gives us: \[ 126 = 2(6w + w) \] Simplifying that, we find: \[ 126 = 2(7w) \] \[ 126 = 14w \] Dividing both sides by 14 yields: \[ w = 9 \text{ yd} \] Now, using this width, we can find the length: \[ \text{length} = 6w = 6 \times 9 = 54 \text{ yd} \] The dimensions of the rectangle are: width: \( 9 \text{ yd} \) and length: \( 54 \text{ yd} \). Now, the width is \( 9 \text{ yd} \). If you’re ever going to create a similar problem in real life, think about things like space for furniture, planning a garden, or even designing a new room! Knowing how to calculate area, perimeter, and dimensions is super handy in interior design or landscaping. One common mistake people often make is forgetting the basic relationship between perimeter and the dimensions of the rectangle. It’s easy to get tangled up in the equations, especially when translating words into numbers, so taking a moment to outline what each variable represents can be a game-changer in problem-solving!