Answer: The width of the room is 36 feet and the length of the room is 48 feet.
Explanation:
To solve this problem using elimination, you can set up a system of equations to represent the information given in the problem.
Let w be the width of the room, and let l be the length of the room. We are told that the length of the room is 12 feet longer than its width, so we can set up the equation:
l = w + 12
We are also told that half the perimeter of the rectangular floor is 72 feet. The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
Since half the perimeter is 72 feet, the full perimeter is 2 * 72 = 144 feet. Substituting the equation for the length of the room, we get:
144 = 2 * (w + 12 + w)
Combining like terms and solving for w, we get:
w = 36
Substituting this value back into the equation for the length of the room, we get:
l = 36 + 12 = 48
Therefore, the width of the room is 36 feet and the length of the room is 48 feet.
To solve this problem using substitution, we could start by solving for the width of the room in one of the equations, and then substituting that value into the other equation to solve for the length of the room.
For example, we could solve the equation l = w + 12 for w to get:
w = l - 12
Substituting this expression for w into the equation for the perimeter, we get:
144 = 2 * (l - 12 + l)
Combining like terms and solving for l, we get:
l = 48
Substituting this value back into the equation for the width of the room, we get:
w = 48 - 12 = 36
Therefore, the width of the room is 36 feet and the length of the room is 48 feet.