the perimeter of a rectangle is to be no greater than 100 centimeters and the length must be 40 centimeters. Find the maximum width of the rectangle.
Let's assume the width of the rectangle is "x" centimeters.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Since the length is given as 40 centimeters, the formula becomes:
Perimeter = 2(40 + x)
According to the given conditions, the perimeter must not exceed 100 centimeters. Therefore, we can write the inequality:
2(40 + x) ≤ 100
Now let's solve this inequality for "x":
80 + 2x ≤ 100
2x ≤ 100 - 80
2x ≤ 20
x ≤ 10
Hence, the maximum width of the rectangle is 10 centimeters.
To find the maximum width of the rectangle, we need to determine the value that satisfies the given conditions.
Let's assume the width of the rectangle is 'w'.
The perimeter of the rectangle is given by the formula:
Perimeter = 2(length + width)
Given that the length of the rectangle is 40 centimeters, the perimeter equation becomes:
100 = 2(40 + w)
Simplifying the equation, we have:
100 = 80 + 2w
Subtracting 80 from both sides of the equation:
20 = 2w
Dividing both sides by 2:
w = 10
Therefore, the maximum width of the rectangle is 10 centimeters.
To find the maximum width of the rectangle, let's use the formula for the perimeter of a rectangle, which is given by the equation:
Perimeter = 2(length + width)
In this problem, the length is given as 40 centimeters, and we want the perimeter to be no greater than 100 centimeters. So we can set up the inequality:
2(40 + width) ≤ 100
Let's solve this inequality step by step:
First, simplify the inequality:
80 + 2(width) ≤ 100
Next, subtract 80 from both sides to isolate the 2(width) term:
2(width) ≤ 20
Then, divide both sides by 2 to solve for width:
width ≤ 10
Therefore, the maximum width of the rectangle is 10 centimeters.