Math Problem Statement
Solution
In this problem, Trapezoid is a scaled copy of Trapezoid . You are tasked with finding the value of , the height of Trapezoid , using the dimensions of both trapezoids.
Given:
- Trapezoid : height = 28, side = 20
- Trapezoid : side = 25, height = (unknown)
To solve this, we need to use the fact that these two trapezoids are similar. In similar figures, the ratio of corresponding sides is constant. This gives us the proportion:
Now, let's solve for :
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Cross-multiply to clear the fraction:
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Simplify:
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Divide both sides by 20 to solve for :
Final Answer:
The value of is 35.
Would you like a detailed breakdown of the steps? Let me know if you have any further questions! Here are some related questions you can explore:
- What is the ratio of the areas of the two trapezoids?
- How would the problem change if only the bases of the trapezoids were scaled?
- What is the ratio of perimeters of Trapezoid and ?
- How do you find the area of a trapezoid, and what would be the areas of both trapezoids?
- How does the concept of scale factor apply to other polygons like triangles or rectangles?
Tip: When working with similar figures, always remember that corresponding sides are proportional!
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Math Problem Analysis
Mathematical Concepts
Geometry
Similar Figures
Proportional Relationships
Formulas
Proportional relationship formula: a/b = c/d
Theorems
Properties of similar figures
Cross-multiplication in proportions
Suitable Grade Level
Grade 7