Final answer:
To find the area of the rectangular label, we need to determine the length and width of the rectangle. By setting up equations using the given information about the length and the perimeter of the rectangle, we can solve for the width. Once we have the width, we can calculate the length and then use the formula for the area of a rectangle to find the area.
Step-by-step explanation:
To find the area of a rectangle, we need to know the length and width of the rectangle. Let's denote the width as 'w'.
The length of the rectangle is 1cm more than twice the width, which can be written as: length = 2w + 1.
The perimeter of a rectangle is given by the formula: perimeter = 2(length + width). We are given that the perimeter is 110cm.
Substituting the values, we get: 110 = 2((2w + 1) + w).
Simplifying the equation gives us: 110 = 6w + 2.
Subtracting 2 from both sides gives: 108 = 6w.
Dividing by 6 gives: 18 = w.
Therefore, the width of the rectangle is 18cm.
Now, substituting the value of width back into the equation for length, we get: length = 2(18) + 1 = 37cm.
The area of the rectangle is given by the formula: area = length * width. Substituting the values, we get: area = 37 * 18 = 666cm^2.
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