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

The width of the room can be represented as \( w \), making the length \( 4w \). The perimeter of a rectangle is calculated as \( 2(\text{length} + \text{width}) \). Plugging in the given values, we have: \[ 2(4w + w) = 50 \] Simplifying gives us: \[ 10w = 50 \] This means \( w = 5 \) meters. Therefore, the length, which is \( 4w \), would be \( 4 \times 5 = 20 \) meters. To reaffirm your finding, the equation checks out with the perimeter: \( 2(20 + 5) = 50 \) meters, thus confirming the dimensions. The length is: 20 meters.