Math Problem Statement
Solution
To solve this problem, let's go through the steps to find the perimeter of the new square after dilation.
Problem Analysis:
-
Given:
- The side of the original square is 8 inches.
- The square is dilated by a scale factor of .
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Find:
- The perimeter of the new square after dilation.
Step-by-Step Solution:
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Calculate the side length of the new square:
The dilation of a shape by a scale factor affects all dimensions. The side length of the original square is multiplied by the scale factor to get the side length of the new square.
Substituting the values:
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Calculate the perimeter of the new square:
The perimeter of a square is given by:
Substituting the new side length:
Conclusion:
The perimeter of the new square after dilation is 8 inches. Therefore, the correct answer is:
D) 8 inches.
Would you like further details or have any questions about this solution?
Related Questions:
- How would the area of the square change with the same dilation factor?
- If the scale factor was instead of , what would the new perimeter be?
- How do dilation and scale factors affect different geometric shapes?
- What would be the side length if the original square had a perimeter of 32 inches instead?
- How do you calculate the perimeter of other polygons after dilation?
Tip:
When dealing with dilation problems, remember that the scale factor directly affects all linear dimensions, such as perimeter, but the area is affected by the square of the scale factor.
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Math Problem Analysis
Mathematical Concepts
Geometry
Dilation
Perimeter
Formulas
New side length = Original side length × Scale factor
Perimeter of square = 4 × side length
Theorems
Properties of Dilation
Suitable Grade Level
Grades 6-8
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