the length of a rectangle is 5 units longer than its width. If the perimeter must be at least 34 units, what are the possible lengths is the rectangle

w ≥ 6

l ≥ 11

Step-by-step explanation:

The perimeter of a rectangle is equal to P = 2l+2w where l=length and w=width. Here the length is 5 feet longer than the width or 5+w. This means the width is w. Substitute P = 34, l=5+w and w into the perimeter equation. Then solve for w.

34 ≤ 2 * (5+w) + 2w

34 ≤ 10+2w+2w

34 ≤ 10+4w

24 ≤ 4w

6 ≤ w

This means the width must be at least 6 so the solution is w ≥ 6.

To find the length substitute 6 into l ≤ 5+w.

l ≤ 5 + 6

l ≤ 11

The length is l ≥ 11.