Question
Use proportions to find the missing side length ( x ) in the two similar figures.
1. Triangle 13 yd and x
2. Triangle 3.25 and 4.23
1. Triangle 13 yd and x
2. Triangle 3.25 and 4.23
Answers
GPT-4o mini
To find the missing side length \( x \) in the two similar triangles using proportions, we can set up a proportion based on the lengths of the sides of the triangles.
Given the two pairs of triangles:
1. For the first pair:
- Triangle 1 has sides \( 13 \, \text{yd} \) and \( x \)
- Triangle 2 has a side of \( 3.25 \).
We can set up the proportion:
\[
\frac{13}{x} = \frac{3.25}{4.23}
\]
To solve for \( x \), we will cross-multiply:
\[
13 \cdot 4.23 = x \cdot 3.25
\]
This simplifies to:
\[
55.19 = 3.25x
\]
Next, solve for \( x \):
\[
x = \frac{55.19}{3.25} \approx 16.95 \, \text{yd}
\]
2. Now using this value of \( x \) (approximately \( 16.95 \, \text{yd} \)), we can analyze the second pair:
For the second triangle pair, we have:
- Triangle 1 side \( x \) (approximately \( 16.95 \, \text{yd} \))
- Triangle 2 side \( 4.23 \)
No new calculation is necessary since we already solved for \( x \) based on the first triangle's parameters.
In conclusion, the missing side length \( x \) is approximately \( 16.95 \, \text{yd} \). If you have specific new figures or constraints in the second triangle pair, please provide them!
Given the two pairs of triangles:
1. For the first pair:
- Triangle 1 has sides \( 13 \, \text{yd} \) and \( x \)
- Triangle 2 has a side of \( 3.25 \).
We can set up the proportion:
\[
\frac{13}{x} = \frac{3.25}{4.23}
\]
To solve for \( x \), we will cross-multiply:
\[
13 \cdot 4.23 = x \cdot 3.25
\]
This simplifies to:
\[
55.19 = 3.25x
\]
Next, solve for \( x \):
\[
x = \frac{55.19}{3.25} \approx 16.95 \, \text{yd}
\]
2. Now using this value of \( x \) (approximately \( 16.95 \, \text{yd} \)), we can analyze the second pair:
For the second triangle pair, we have:
- Triangle 1 side \( x \) (approximately \( 16.95 \, \text{yd} \))
- Triangle 2 side \( 4.23 \)
No new calculation is necessary since we already solved for \( x \) based on the first triangle's parameters.
In conclusion, the missing side length \( x \) is approximately \( 16.95 \, \text{yd} \). If you have specific new figures or constraints in the second triangle pair, please provide them!