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.