Question

use proportions to find the missing side length x in the two similar figures 13yd. 3.25yd. 4.23 yd.

Answer 1

To find the missing side length \( x \) in two similar figures using proportions, we can set up a proportion based on the corresponding sides of the similar figures.

Let’s assign the known lengths:
- Let \( a = 13 \) yd (side length from one figure)
- Let \( b = 3.25 \) yd (side length from another figure)
- Let \( c = 4.23 \) yd (the other side length from the second figure)
- Let \( x \) be the corresponding side length we want to find.

Because the figures are similar, we can write the proportion as follows:

\[
\frac{13}{x} = \frac{3.25}{4.23}
\]

Now let's solve for \( x \).

1. Cross-multiply:
\[
13 \cdot 4.23 = 3.25 \cdot x
\]

2. Calculate \( 13 \cdot 4.23 \):
\[
13 \cdot 4.23 = 55.99
\]

3. Substitute back into the equation:
\[
55.99 = 3.25 \cdot x
\]

4. Now, solve for \( x \):
\[
x = \frac{55.99}{3.25}
\]

5. Calculate:
\[
x \approx 17.23 \, \text{yd}
\]

Thus, the missing side length \( x \) is approximately \( 17.23 \) yd.