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?

A. 2w+2 x (46) _< 106

B. 2w + 2 x (4) _> 106

C. 2w+2 x (4w) < 106

D. 2w+2 x (46) > 106

Answer: A

Step-by-step explanation: The answer is w≤ 13, which means that the greatest value possible is 13.

Greatest possible value for the width is 10.6 centimeters.

D. 2w+2 * (46) > 106

Step-by-step explanation:

Perimeter of a rectangle = 2 (l + w)

From the given question, P = 106 and l = 4w

So that,

106 = 2 (4w + w)

106 = 2 (5w)

106 = 10 w

w = 10.6 centimeters

So, the greatest possible value for the width is 10.6 centimeters.

Model; 2w+2 * (46) > 106

= 2 * 10.6 + 2 * (46)

= 113.2

113.2 is greater than 106