Answer:
width: 10 centimeters
length: 38 centimeters
Explanation:
Let's start by assigning variables to the width and length of the frame.
Let x be the width of the frame in centimeters.
Then, according to the problem statement, the length of the frame is 18 centimeters more than double the width, which can be expressed as 2x + 18.
The perimeter of a rectangle is the sum of the lengths of all four sides, so the perimeter of this frame is:
2(length + width) = 2(2x + 18 + x) = 6x + 36
We know that the perimeter of the frame is 96 centimeters, so we can set up an equation:
6x + 36 = 96
Simplifying this equation, we get:
6x = 60
x = 10
So the width of the frame is 10 centimeters.
To find the length, we can plug x = 10 into the expression we found earlier for the length:
length = 2x + 18 = 2(10) + 18 = 38
So the length of the frame is 38 centimeters.
Therefore, the width of the frame is 10 centimeters and the length is 38 centimeters.