Answer:
Width = 10 feet
Length = 16.5 feet
Explanation:
We can determine the length and width of the room using a system of equations where:
- L represents the room's length,
- and W represents its width.
First equation:
The formula for 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.
Since we're told that the room's perimeter is 53 feet, our first equation is given by:
53 = 2L + 2W
Second equation:
Since we're told that the room's length is 3.5 feet less than twice the width, our second equation is given by:
L = 2W - 3.5
Method to solve: Substitution:
Solving for W (the width):
Now we can solve for W (the width) by substituting 2W - 3.5 for L in the first equation in our system:
53 = 2(2W - 3.5) + 2W
53 = 4W - 7 + 2W
(53 = 6W - 7) + 7
(60 = 6W) / 6
10 = W
Thus, the width is 10 feet.
Solving for L (the length):
Now we can solve for L (the length) by plugging in 10 for W in the second equation in our system:
L = 2(10) - 3.5
L = 20 - 3.5
L = 16.5
Thus, the length is 16.5 feet.