Question

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.
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Part 1
x cm40 cm
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Part 1
​First, understand the problem. Then translate the statement into an inequality.
the perimeter
of the rectangle

is less than or equal to

90
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Answer 1

The perimeter of a rectangle is calculated by adding up all four sides. In this case, we have one side with the length of 40 cm, and the other side is represented by the variable x. Therefore, the perimeter can be represented as:

Perimeter = 40 + x + 40 + x

To ensure that the perimeter is no greater than 90 cm, we can write the inequality:

40 + x + 40 + x ≤ 90

Simplifying the inequality:

80 + 2x ≤ 90

Subtracting 80 from both sides:

2x ≤ 10

Dividing both sides by 2:

x ≤ 5

Therefore, the maximum width of the rectangle (represented by the variable x) is 5 cm.