Question

The length of a rectangle is 10 feet less than it's width. The maximum perimeter of the rectangle

should be 60 feet. Write an inequality to represent this.

Answer 1

To write an inequality that represents the maximum perimeter of the rectangle, set up the inequality 2(W - 10) + 2W ≤ 60 and solve for W ≤ 20. This means the width of the rectangle should be less than or equal to 20 feet.

Step-by-step explanation:

To write an inequality that represents the maximum perimeter of the rectangle, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In this case, we are given that the length is 10 feet less than the width, so we can express the length as W - 10. Additionally, the maximum perimeter should be 60 feet, so we can set up the inequality as follows:

2(W - 10) + 2W ≤ 60

Next, we can simplify and solve the inequality:

2W - 20 + 2W ≤ 60

4W - 20 ≤ 60

4W ≤ 80

W ≤ 20

Therefore, the inequality that represents the maximum perimeter of the rectangle is W ≤ 20. This means that the width of the rectangle should be less than or equal to 20 feet in order for the perimeter to be at most 60 feet.