The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. Find the length and width of the rectangle. If \( w= \) the width of the rectangle, then the length equals \( 4 w \) \( w-4 \) \( w+4 \)

To find the dimensions of the rectangle, let's use the given information! Let \( w \) be the width. According to the problem, the length is \( w + 4 \). The formula for the perimeter of a rectangle is \( P = 2(\text{length} + \text{width}) \). Substituting the known values, we have: \[ 34 = 2((w + 4) + w) \] \[ 34 = 2(2w + 4) \] \[ 34 = 4w + 8 \] \[ 26 = 4w \] \[ w = 6.5 \text{ inches} \] The length then will be \( 6.5 + 4 = 10.5 \text{ inches} \). So, the width is 6.5 inches, and the length is 10.5 inches! Now, here's a twist: in historical contexts, rectangles have played crucial roles in architecture and agriculture, from ancient Egypt’s land division using geometric principles to modern landscaping. Isn’t it cool that math has been used to build magnificent structures from the pyramids to skyscrapers? Moreover, in practical terms, knowing how to calculate the perimeter and dimensions of rectangles can be invaluable in everyday tasks like planning furniture arrangements or designing home improvements. Understanding these concepts can help save money by optimizing space usage!