Question
Find the ratio of the corresponding sides of the given similar triangles.
31.5
8
35
9
10
28
Question content area bottom
Part 1
The ratio of the corresponding sides of the triangle on the left to the triangle on the right is
enter your response here.
(Type the ratio as a simplified fraction.)
31.5
8
35
9
10
28
Question content area bottom
Part 1
The ratio of the corresponding sides of the triangle on the left to the triangle on the right is
enter your response here.
(Type the ratio as a simplified fraction.)
Answers
GPT-4o mini
To find the ratio of the corresponding sides of the two similar triangles, we need to pair the lengths of their corresponding sides together and simplify the fractions.
Given the pairs of lengths:
- First triangle: 31.5 and 35
- Second triangle: 8 and 9
- Third triangle: 10 and 28
We will calculate the ratios for each pair:
1. For the first pair:
\[
\text{Ratio} = \frac{31.5}{35}
\]
To simplify this, we can divide both the numerator and denominator by 7:
\[
\frac{31.5 \div 7}{35 \div 7} = \frac{4.5}{5} = \frac{9}{10}
\]
2. For the second pair:
\[
\text{Ratio} = \frac{8}{9}
\]
This ratio is already in simplest form.
3. For the third pair:
\[
\text{Ratio} = \frac{10}{28}
\]
To simplify this, we divide both the numerator and denominator by 2:
\[
\frac{10 \div 2}{28 \div 2} = \frac{5}{14}
\]
Now, we have the ratios:
- First pair: \(\frac{9}{10}\)
- Second pair: \(\frac{8}{9}\)
- Third pair: \(\frac{5}{14}\)
Since these triangles are similar, all their corresponding side ratios should be equivalent. If we find a common ratio based only on the first pair, you can express all other ratios accordingly.
However, as different pairs have different ratios and only one pair is equivalent among similar triangles, you could either choose the one you prefer or recognize that if they correspond differently, then the similarity condition is not fulfilled completely through all three.
If you need only one ratio for final submission, the one from the first pair helps establish a connection:
**The ratio of the corresponding sides of the triangle on the left to the triangle on the right is \(\frac{9}{10}\)**.
Given the pairs of lengths:
- First triangle: 31.5 and 35
- Second triangle: 8 and 9
- Third triangle: 10 and 28
We will calculate the ratios for each pair:
1. For the first pair:
\[
\text{Ratio} = \frac{31.5}{35}
\]
To simplify this, we can divide both the numerator and denominator by 7:
\[
\frac{31.5 \div 7}{35 \div 7} = \frac{4.5}{5} = \frac{9}{10}
\]
2. For the second pair:
\[
\text{Ratio} = \frac{8}{9}
\]
This ratio is already in simplest form.
3. For the third pair:
\[
\text{Ratio} = \frac{10}{28}
\]
To simplify this, we divide both the numerator and denominator by 2:
\[
\frac{10 \div 2}{28 \div 2} = \frac{5}{14}
\]
Now, we have the ratios:
- First pair: \(\frac{9}{10}\)
- Second pair: \(\frac{8}{9}\)
- Third pair: \(\frac{5}{14}\)
Since these triangles are similar, all their corresponding side ratios should be equivalent. If we find a common ratio based only on the first pair, you can express all other ratios accordingly.
However, as different pairs have different ratios and only one pair is equivalent among similar triangles, you could either choose the one you prefer or recognize that if they correspond differently, then the similarity condition is not fulfilled completely through all three.
If you need only one ratio for final submission, the one from the first pair helps establish a connection:
**The ratio of the corresponding sides of the triangle on the left to the triangle on the right is \(\frac{9}{10}\)**.