The width of a rectangle is 30 centimeters. Find all possible values for the length of the rectangle if the perimeter is at least 768 centimeters.

there are infinitely many possible values:

2(30+L) >= 768
30+L >= 384
L >= 354

so, any number at least 354 will work.

I suspect you did not ask the right question.

P = 2L + 2W

768 <= 2L + (2 * 30)

768 <= 2L + 60

708 <= 2L

354 >= L

To find all possible values for the length 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.

Given that the width of the rectangle is 30 centimeters, we can substitute the values into the formula:

P = 2L + 2(30)

Since we know that the perimeter is at least 768, we can write the inequality:

768 ≤ 2L + 2(30)

Simplifying the equation, we have:

768 ≤ 2L + 60

Subtracting 60 from both sides:

708 ≤ 2L

Dividing both sides by 2:

354 ≤ L

Therefore, the length of the rectangle must be equal to or greater than 354 centimeters.

Hence, all possible values for the length of the rectangle are L ≥ 354 centimeters.