Question

The polygons to the right are similar. Find the value of each variable.
28
21
35
5
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Part 1
xequals
  
enter your response here
yequals
  
enter your response here
​(Simplify your​ answers.)

Answer 1

To solve for \( x \) and \( y \) in similar polygons, we'll use the property that corresponding sides of similar polygons are in proportion. This means that the ratios of corresponding sides are equal.

Given the data you provided:

1. The lengths of one polygon are 28 and 21.
2. The lengths of the corresponding sides of the other polygon are 35 and 5.

Using the proportionality of the sides, we can set up two equations.

For \( x \), corresponding to the side lengths 28 and 35:
\[
\frac{28}{35} = \frac{x}{5}
\]

Cross-multiplying gives:
\[
28 \cdot 5 = 35 \cdot x
\]
\[
140 = 35x
\]
Now, divide both sides by 35:
\[
x = \frac{140}{35} = 4
\]

Now, for \( y \), corresponding to the side lengths 21 and 28:
\[
\frac{21}{28} = \frac{y}{35}
\]

Cross-multiplying gives:
\[
21 \cdot 35 = 28 \cdot y
\]
\[
735 = 28y
\]
Now, divide both sides by 28:
\[
y = \frac{735}{28} = 26.25
\]

Thus, the values are:
- \( x = 4 \)
- \( y = 26.25 \)

**Final Answers:**
\( x = 4 \)

\( y = 26.25 \)