Final answer:
To find the greatest dimensions of the rectangle, set up an equation using given information. Find the values that satisfy the inequality and check the given answer choices.
Step-by-step explanation:
To find the greatest possible dimensions of the rectangle, we can set up an equation using the given information. Let's represent the width of the rectangle as 'w' and the length as 'l'. The problem states that the length is 3 more than twice the width, so we can write the equation as l = 2w + 3.
The perimeter of a rectangle is given by the formula P = 2(l + w). We are told that the perimeter is not greater than 64, so we can set up the inequality 2(l + w) ≤ 64.
Substituting the equation for l into the inequality, we get 2((2w + 3) + w) ≤ 64. Simplifying, we have 2(3w + 3) ≤ 64. Solving for w, we find that w ≤ 15.
We can now check the given answer choices to find the greatest possible dimensions of the rectangle. Option a has a width of 15, which satisfies the inequality, and a length of 30 (2(15) + 3), so the correct answer is: a. Length: 30, Width: 15.