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
The maximum width of the rectangle can be represented by the variable X.
The perimeter of the rectangle is equal to 2(length + width), so we can write the inequality as:
2(40 + X) ≤ 130
Simplifying the inequality:
80 + 2X ≤ 130
Subtracting 80 from both sides:
2X ≤ 130 - 80
2X ≤ 50
Dividing both sides by 2:
X ≤ 25
Therefore, the maximum width of the rectangle is 25 centimeters.
To find the maximum width of the rectangle, we need to set up an inequality using the given information.
Let's denote the width of the rectangle as W.
Since the perimeter of a rectangle is equal to the sum of all its sides, we can write the inequality as:
2(40 + W) ≤ 130
This is because the perimeter of a rectangle is calculated by adding twice the length and twice the width.
Now, let's solve the inequality step by step.
To find the maximum width of the rectangle, we need to set up an inequality based on the given information.
Let's call the width of the rectangle "W". The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the rectangle has two sides of length 40 cm and two sides of length W cm.
Therefore, the perimeter of the rectangle is given by the equation:
Perimeter = 2 * Length + 2 * Width
Substituting the given length (40 cm) and the width (W cm) into the equation, we get:
Perimeter = 2 * 40 + 2 * W
Simplifying further:
Perimeter = 80 + 2W
The problem states that the perimeter of the rectangle must be no greater than 130 cm. Inequality is used to represent this statement.
Perimeter ≤ 130
Substituting the equation for perimeter, we have:
80 + 2W ≤ 130
Now we can solve the inequality to find the maximum width of the rectangle.
First, subtract 80 from both sides of the inequality:
2W ≤ 130 - 80
2W ≤ 50
Next, divide both sides of the inequality by 2:
W ≤ 25
So, the maximum width of the rectangle is 25 centimeters.