Math Problem Statement

Trapezoid G is a scaled copy of trapezoid F. Given that trapezoid F has a height of 28 and a side length of 20, and trapezoid G has a side length of 25, what is the value of h (the height of trapezoid G)?

Solution

In this problem, Trapezoid GG is a scaled copy of Trapezoid FF. You are tasked with finding the value of hh, the height of Trapezoid GG, using the dimensions of both trapezoids.

Given:

  • Trapezoid FF: height = 28, side = 20
  • Trapezoid GG: side = 25, height = hh (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:

2025=28h\frac{20}{25} = \frac{28}{h}

Now, let's solve for hh:

  1. Cross-multiply to clear the fraction: 20h=28×2520h = 28 \times 25

  2. Simplify: 20h=70020h = 700

  3. Divide both sides by 20 to solve for hh: h=70020=35h = \frac{700}{20} = 35

Final Answer:

The value of hh 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:

  1. What is the ratio of the areas of the two trapezoids?
  2. How would the problem change if only the bases of the trapezoids were scaled?
  3. What is the ratio of perimeters of Trapezoid FF and GG?
  4. How do you find the area of a trapezoid, and what would be the areas of both trapezoids?
  5. 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