Math Problem Statement
Solution
In the image provided, we are given two quadrilaterals, and , where quadrilateral is a scaled copy of quadrilateral . The side lengths of quadrilateral are 40, 40, 45, and some unknown side. In quadrilateral , the corresponding side lengths are 32, 32, and the unknown side labeled .
To find the value of :
Since is a scaled copy of , we can use the ratio of corresponding sides to find .
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Compare the corresponding sides of and . The two known sides in quadrilateral are both 40, and the corresponding sides in are both 32.
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Now, apply this scale factor to the unknown side in quadrilateral to find in quadrilateral .
Thus, the value of is 36.
Would you like further details or explanations?
Related Questions:
- How do you determine the scale factor between two similar figures?
- What is the relationship between corresponding sides of similar polygons?
- How can you verify that two polygons are similar?
- What are the properties of quadrilaterals that help in determining similarity?
- How would the calculation change if one side of quadrilateral was unknown?
Tip:
Always ensure that corresponding sides of similar polygons are compared when determining scale factors or unknown lengths.
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Math Problem Analysis
Mathematical Concepts
Proportions
Scale Factor
Geometry
Formulas
Scale factor = Corresponding side of H / Corresponding side of G
i = Scale factor × Unknown side in G
Theorems
Similarity Theorem for polygons
Proportionality Theorem
Suitable Grade Level
Grade 7