Question

The length of a rectangle is four times its width. If the perimeter is at most 106 centimeters, what is the greatest possible value for the width?

Which inequality models this problem?


Options:
A. 2w + 2 (4W) - 106
B. 2w + 2.(4W) 2 106
C. 2w+ 2 (4w) < 106
D. 2W + 2. (4w) > 106

Answer 1

To find the greatest possible value for the width of the rectangle, we can set up an equation and solve an inequality. The inequality that models this problem is 2w + 2(4w) < 106.

Step-by-step explanation:

To solve this problem, we can set up an equation using the given information. Let's say the width of the rectangle is 'w'. According to the problem, the length of the rectangle is four times its width, so the length would be '4w'.

The perimeter of a rectangle is calculated by adding all four sides. For this rectangle, the perimeter would be 2w + 2(4w) = 10w.

Since the perimeter is at most 106 centimeters, we can set up the inequality: 10w ≤ 106. Solving this inequality will give us the maximum possible value for 'w'. Therefore, the inequality that models this problem is C. 2w + 2(4w) < 106.