Math Problem Statement
Solution
To determine the scale factor for each part of this problem, let's analyze each figure separately:
Part (a)
In part (a), we have two rectangles, ABCD and EFGC. Rectangle ABCD is a smaller rectangle within EFGC.
- The dimensions of rectangle ABCD are given as by .
- The dimensions of rectangle EFGC are not directly provided, but since it appears that the larger rectangle doubles the dimensions of ABCD in each direction, we assume:
- Height:
- Width:
Thus, the scale factor from ABCD to EFGC is: So, the scale factor is .
Part (b)
In part (b), we have two triangles, and , with being an enlargement of .
- In , side and .
- In , which is the smaller triangle, side is assumed to be the corresponding side to in .
Since and : Thus, the scale factor from to is also .
Summary
- Scale factor for part (a):
- Scale factor for part (b):
Would you like further explanations on how scale factors work or have any additional questions?
Related Questions
- How would the scale factor change if only one dimension of the figures doubled?
- What happens to the area of a shape if the scale factor is doubled?
- Can you determine the scale factor if only the areas of two similar figures are given?
- How would you calculate the scale factor if given the perimeters of similar figures?
- What is the impact of the scale factor on the angles of similar figures?
Tip
When working with similar figures, remember that corresponding sides are proportional, but angles remain unchanged.
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Math Problem Analysis
Mathematical Concepts
Scale Factor
Similar Figures
Proportions
Formulas
Scale factor = Length of larger figure / Length of smaller figure
Theorems
Properties of Similar Figures
Suitable Grade Level
Grades 7-9