The perimeter of a rectangle is to be no greater than 130 centimeters and the length must be 40 centimeters. Find the maximum width of the rectangle.
First, understand the problem. Then translate the statement into an inequality.
the perimeter of the rectangle x+40+_
is less than or equal to —> _
130 —>130
- (x + 40)
To find the maximum width of the rectangle, we can use the formula for the perimeter of a rectangle which is P = 2(length + width).
In this case, the length is given as 40 centimeters and the perimeter should not exceed 130 centimeters. So we have:
130 ≥ 2(40 + width)
Now, let's simplify the equation:
130 ≥ 80 + 2width
Subtract 80 from both sides:
130 - 80 ≥ 80 - 80 + 2width
50 ≥ 2width
Divide both sides by 2:
50/2 ≥ 2width/2
25 ≥ width
Therefore, the maximum width of the rectangle is 25 centimeters.
To find the maximum width of the rectangle, we need to solve the inequality that represents the perimeter of the rectangle being no greater than 130 centimeters.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
We are given that the length of the rectangle is 40 centimeters. Let's denote the width as 'w'.
Putting this into the inequality, we have:
2 * (40 + w) ≤ 130
Now, let's solve this inequality step by step:
Step 1: Simplify the expression inside the parentheses:
80 + 2w ≤ 130
Step 2: Move the constant term (80) to the right side of the inequality by subtracting it from both sides:
2w ≤ 130 - 80
2w ≤ 50
Step 3: Divide both sides of the inequality by 2 to isolate 'w':
w ≤ 50 / 2
w ≤ 25
Therefore, the maximum width of the rectangle is 25 centimeters.