The perimeter of a rectangle is to be no greater than 90 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 recatgle is less than or equal to 90
x+40+ blank blank 90
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
In this case, the length is given as 40 centimeters. Let's substitute this value into the formula:
P = 2(40) + 2w
However, the problem states that the perimeter must be no greater than 90 centimeters. So, we can set up the following inequality:
2(40) + 2w ≤ 90
Simplifying this inequality, we get:
80 + 2w ≤ 90
Subtracting 80 from both sides, we have:
2w ≤ 10
To find the maximum width, we divide both sides of the inequality by 2:
w ≤ 5
Therefore, the maximum width of the rectangle is 5 centimeters.