The length of a rectangle is 10 meters less than 4 times its width. If the perimeter of the rectangle is at most 120 meters, what is the greatest possible width of the rectangle?
To find the greatest possible width of the rectangle, we need to solve the problem step by step.
Let's start by assigning variables to the dimensions of the rectangle:
Let w be the width of the rectangle.
The length of the rectangle is 4w - 10 (10 meters less than 4 times its width).
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
In this case, the perimeter is at most 120 meters, so we can write the inequality:
2 * (4w - 10 + w) ≤ 120
Simplifying the inequality, we get:
2 * (5w - 10) ≤ 120
10w - 20 ≤ 120
10w ≤ 140
w ≤ 14
So, the width of the rectangle must be less than or equal to 14 meters.
Therefore, the greatest possible width of the rectangle is 14 meters.
2(w + 4w-10) <= 120
5w - 10 <= 60
now finish it off