Final answer:
By representing the width with w and creating an inequality from the given information, the width w is found to be at most 12 inches. Substituting this into the length formula, the greatest possible measure of the length of the rectangle is determined to be 17 inches.
Step-by-step explanation:
To find the greatest possible measure of the length of the rectangle, let's denote the width as w inches. According to the problem, the length l is seven less than twice its width, so l = 2w - 7. The perimeter P of a rectangle is given by P = 2l + 2w. Since the perimeter is at most 58 inches, we have 2(2w - 7) + 2w ≤ 58. Simplifying this inequality:
- 4w - 14 + 2w ≤ 58
- 6w - 14 ≤ 58
- 6w ≤ 72
- w ≤ 12
Therefore, the width w is at most 12 inches. To find the greatest possible length, substitute w = 12 into the length formula:
- l = 2(12) - 7
- l = 24 - 7
- l = 17
So, the greatest possible length of the rectangle is 17 inches.