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 : meters and the width is Check Answer

To solve for the dimensions of the room, we can start by letting the width be \( w \) meters. Since the length is 4 times the width, we express the length as \( 4w \). The formula for the perimeter \( P \) of a rectangle is given by \( P = 2(\text{length} + \text{width}) \). Setting up the equation: \[ 50 = 2(4w + w) \] \[ 50 = 2(5w) \] \[ 50 = 10w \] \[ w = 5 \] Thus, the width is 5 meters, and the length is: \[ 4w = 4 \times 5 = 20 \text{ meters} \] The length is 20 meters, and the width is 5 meters. --- The concept of rectangles goes way back in history! The ancient Egyptians structured their land plots in rectangular shapes and used the 3-4-5 triangle method for creating right angles, ensuring their fields were accurately measured. This geometric knowledge helped in building structures, regulating land, and even drafting architectural plans for temples! When calculating dimensions, one common mistake is misinterpreting the relationship between length and width, especially in word problems. Always carefully define your variables and double-check that they align with the given information! For instance, if you mistakenly assigned the length as the width and vice versa, your calculations might lead to incorrect dimensions.