Final answer:
To find the dimensions of the rectangular room with twice the length of its width and a perimeter of 36 meters, we deduce the width is 6 meters, and the length is 12 meters.
Step-by-step explanation:
Assuming a rectangular room is twice as long as it is wide, and given that its perimeter is 36 meters, we can find its dimensions as follows:
Let the width be w meters.
Then the length is 2w meters (since it's twice the width).The perimeter of a rectangle is given by P = 2l + 2w where P is the perimeter, l is the length, and w is the width.Substitute the known values to get 36 = 2(2w) + 2w = 6w.Solving for w, we get w = 36 / 6 = 6 meters.Therefore, the length is 2w = 2(6) = 12 meters.
-
The dimensions of the room are thus 6 meters wide and 12 meters long.
To find the dimensions of the rectangular room, we'll solve the system of equations that represents the given information. Let the width of the room be 'w' meters. Since the length is two times the width, the length would be '2w' meters. The perimeter of a rectangle is calculated by adding all four sides, which in this case is: P = 2w + 2(2w) = 36 m. Simplifying this equation, we get: 6w = 36 m. Dividing both sides by 6, we get: w = 6 m. Therefore, the width of the room is 6 meters and the length is 2w = 2(6) = 12 meters.