The length of a rectangle is four times its width. If the perimeter is at most 130 centimeters, what is the greatest possible value for the width?
13 cm
21.7 cm
26 cm
52 cm
(2 * 4W) + 2W < 130
10W < 130
W < 13
Let's assume that the width of the rectangle is "x" centimeters. Since the length is four times the width, the length would be 4x centimeters.
The formula for the perimeter of a rectangle is given by P = 2(length + width).
In this case, the perimeter is at most 130 centimeters, so we have the inequality:
2(4x + x) <= 130
Simplifying the equation, we get:
2(5x) <= 130
10x <= 130
x <= 13
So, the width of the rectangle, "x", can be at most 13 centimeters.
Therefore, the greatest possible value for the width is 13 cm.
Therefore, the correct answer is option A: 13 cm.
To solve this problem, we need to use the formula for the perimeter of a rectangle and the given information.
Let's assume that the width of the rectangle is "w" centimeters.
According to the problem, the length of the rectangle is four times its width. Therefore, the length of the rectangle would be 4w centimeters.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Now we can substitute the values into the equation and solve for the width:
130 cm ≥ 2 * (4w + w)
Dividing both sides of the equation by 2, we get:
65 cm ≥ 5w
Dividing both sides of the equation by 5, we get:
13 cm ≥ w
From the given answer choices, the greatest possible value for the width is 13 cm. Therefore, the correct answer is 13 cm.