Final answer:
The problem involves using the given perimeter and relationship between length and width of a rectangle to create and solve equations for their values. With the width denoted as w, the length is w + 8. Solving this system using the formula for the rectangle's perimeter reveals that the rectangle's width is 22, and length is 30.
Step-by-step explanation:
The subject of this question is geometry, particularly focusing on the properties of rectangles. From the given problem, we know that the perimeter of a rectangle, which is the sum of all its sides, equals 64, and that the length of the rectangle is 8 more than the width. We can use this information to set up equations that will help us find the dimensions of the rectangle.
First, let's denote the width of the rectangle as w. According to the problem, the length is 8 more than the width, so we can define the length as w + 8. The formula for the perimeter of a rectangle is 2*(length + width), so we can set that equal to 64: 2*(w + (w+8)) = 64. Solving this equation for w gives w = 22, so the width of the rectangle is 22.
Since the length is 8 more than the width, we can use that information to find the length: w + 8 = 22 + 8 = 30. Therefore, the length of the rectangle is 30.
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