Math Problem Statement

What is the value of i in the scaled quadrilateral problem, where quadrilateral H is a scaled copy of quadrilateral G, with side lengths 40, 40, 45 in G and corresponding sides 32, 32 in H?

Solution

In the image provided, we are given two quadrilaterals, GG and HH, where quadrilateral HH is a scaled copy of quadrilateral GG. The side lengths of quadrilateral GG are 40, 40, 45, and some unknown side. In quadrilateral HH, the corresponding side lengths are 32, 32, and the unknown side labeled ii.

To find the value of ii:

Since HH is a scaled copy of GG, we can use the ratio of corresponding sides to find ii.

  1. Compare the corresponding sides of GG and HH. The two known sides in quadrilateral GG are both 40, and the corresponding sides in HH are both 32.

    Scale factor=3240=45\text{Scale factor} = \frac{32}{40} = \frac{4}{5}

  2. Now, apply this scale factor to the unknown side 4545 in quadrilateral GG to find ii in quadrilateral HH.

    i=45×45=36i = \frac{4}{5} \times 45 = 36

Thus, the value of ii is 36.

Would you like further details or explanations?

Related Questions:

  1. How do you determine the scale factor between two similar figures?
  2. What is the relationship between corresponding sides of similar polygons?
  3. How can you verify that two polygons are similar?
  4. What are the properties of quadrilaterals that help in determining similarity?
  5. How would the calculation change if one side of quadrilateral GG 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