The length of a picture frame is 8 inches more than the width. For what values of x is the perimeter of the picture frame greater than 160 inches?
Let's denote the width of the picture frame as x inches. According to the given information, the length of the picture frame is 8 inches more than the width. Therefore, the length can be represented as (x + 8) inches.
The perimeter of a rectangle can be calculated by adding all the sides. So, the perimeter of the picture frame can be calculated as follows:
Perimeter = 2(length) + 2(width)
Perimeter = 2(x + 8) + 2x
Perimeter = 2x + 16 + 2x
Perimeter = 4x + 16
Now, we need to find the values of x for which the perimeter is greater than 160 inches. Let's set up the inequality:
4x + 16 > 160
Subtracting 16 from both sides:
4x > 144
Dividing both sides by 4:
x > 36
Therefore, the width of the picture frame must be greater than 36 inches for the perimeter to be greater than 160 inches.
To find the values of 'x' for which the perimeter of the picture frame is greater than 160 inches, we need to first express the width and length of the frame in terms of 'x'.
Let's assume that the width of the frame is 'x' inches. According to the given information, the length of the frame is 8 inches more than the width. Therefore, the length can be expressed as 'x + 8' inches.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
Substituting the values of length and width we obtained earlier:
Perimeter = 2 * (x + 8 + x)
Perimeter = 2 * (2x + 8)
Perimeter = 4x + 16
To find the values of 'x' for which the perimeter is greater than 160 inches, we can set up an inequality:
4x + 16 > 160
Now, we can solve this inequality to find the range of 'x' values:
4x > 160 - 16
4x > 144
x > 144/4
x > 36
Therefore, the values of 'x' for which the perimeter of the picture frame is greater than 160 inches are x > 36.
assuming x is the width,
2(x + 2x+8) >= 160
x >= 24