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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down arrow
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ModifyingAbove x plus 40 plus nothing with brace
▼
greater than
less than or equals
less than
greater than or equals
90
To find the maximum width of the rectangle, let's use variables to represent the width and length of the rectangle. Let's say "x" represents the width of the rectangle (in centimeters) and "40" represents the length of the rectangle (since it is given as 40 centimeters).
The formula for the perimeter of a rectangle is P = 2(length + width). In this case, the perimeter should be no greater than 90 centimeters.
So we can write the inequality as:
2(40 + x) ≤ 90
To solve this, we'll follow these steps:
1. Distribute the 2 across the parentheses:
80 + 2x ≤ 90
2. Subtract 80 from both sides of the inequality:
2x ≤ 90 - 80
2x ≤ 10
3. Divide both sides of the inequality by 2:
x ≤ 10/2
x ≤ 5
Therefore, the maximum width of the rectangle is 5 centimeters.