The length of a picture frame is 6 inches more than the width. For what values of x is the perimeter of the picture frame greater than 152 inches?
To find the values of x for which the perimeter of the picture frame is greater than 152 inches, we need to create an equation that represents the perimeter.
Let's assume the width of the picture frame is x inches.
Since the length is 6 inches more than the width, the length would be x + 6 inches.
The perimeter of a rectangle is given by the formula: P = 2(length + width)
Substituting the values, we have:
P = 2(x + 6 + x)
P = 2(2x + 6)
P = 4x + 12
Now, we can set up the inequality representing the condition that the perimeter is greater than 152 inches:
4x + 12 > 152
To solve this inequality, we can start by subtracting 12 from both sides:
4x > 152 - 12
4x > 140
Next, divide both sides by 4:
x > 140 / 4
x > 35
Therefore, the values of x for which the perimeter of the picture frame is greater than 152 inches are x > 35.
To find the values of x for which the perimeter of the picture frame is greater than 152 inches, let's first express the length and width in terms of x.
Let's assume that x represents the width of the picture frame. According to the given information, the length is 6 inches more than the width. So, the length would be x + 6.
The formula for calculating the perimeter is P = 2(length + width). Substitute the values we just found into the formula:
P = 2(x + (x + 6)) = 2(2x + 6) = 4x + 12.
Now, we have the expression for the perimeter in terms of x: 4x + 12.
To find the values of x for which the perimeter is greater than 152 inches, we need to solve the inequality:
4x + 12 > 152.
Let's solve the inequality step by step:
4x + 12 > 152
4x > 152 - 12
4x > 140
x > 140/4
x > 35.
Therefore, any value of x greater than 35 will make the perimeter of the picture frame greater than 152 inches.
L = W + 6
L * W = (W+6) * W = 152
W^2 + 6W -152 = 0
Factor and solve for W.