A rectangular room is 4 times as long as it is wide, and its perimeter is 50 meters. Find the dimensions of the room. The length is: meters and the width is

To solve this, let the width of the room be \( w \) meters. Since the room is 4 times as long as it is wide, the length will be \( 4w \) meters. The formula for the perimeter \( P \) of a rectangle is \( P = 2 \times (length + width) \). Substituting the known values, we have: \[ 50 = 2 \times (4w + w) \] \[ 50 = 2 \times 5w \] \[ 50 = 10w \] \[ w = 5 \text{ meters (width)} \] Now, to find the length: \[ length = 4w = 4 \times 5 = 20 \text{ meters} \] The dimensions of the room are: Length: 20 meters and Width: 5 meters. When it comes to room design, understanding the proportions can lead to a harmonious space. A room with a 4:1 ratio is often considered visually pleasing and can make a small space feel larger and more inviting. Think about furniture layout too; with a longer room like this, creating separate zones for different activities can enhance its functionality. In terms of construction or interior design, a room's dimensions significantly affect acoustics and lighting. Wider rooms often have better sound distribution while the length can lend itself to strategic window placement. Exploring this can lead to choosing the right colors and materials to enhance both comfort and aesthetics in your space.