Question
If ΔABC is similar to ΔDEF , and AB= 16, DF= 3, and AC= 12, what is the length of DE ?
Answers
GPT-4o mini
Since triangles ΔABC and ΔDEF are similar, the corresponding sides are in proportion. This means that the ratio of the lengths of corresponding sides is constant.
Given:
- \( AB = 16 \)
- \( DF = 3 \)
- \( AC = 12 \)
- Let \( DE \) be the length we need to find.
The ratio of the sides can be represented as:
\[
\frac{AB}{DF} = \frac{AC}{DE}
\]
Substituting the known values into the equation, we have:
\[
\frac{16}{3} = \frac{12}{DE}
\]
Now, we can cross-multiply to solve for \( DE \):
\[
16 \cdot DE = 3 \cdot 12
\]
Calculating the right side:
\[
16 \cdot DE = 36
\]
Now, divide both sides by 16 to isolate \( DE \):
\[
DE = \frac{36}{16} = \frac{9}{4} = 2.25
\]
Thus, the length of \( DE \) is \( \frac{9}{4} \) or \( 2.25 \).
Given:
- \( AB = 16 \)
- \( DF = 3 \)
- \( AC = 12 \)
- Let \( DE \) be the length we need to find.
The ratio of the sides can be represented as:
\[
\frac{AB}{DF} = \frac{AC}{DE}
\]
Substituting the known values into the equation, we have:
\[
\frac{16}{3} = \frac{12}{DE}
\]
Now, we can cross-multiply to solve for \( DE \):
\[
16 \cdot DE = 3 \cdot 12
\]
Calculating the right side:
\[
16 \cdot DE = 36
\]
Now, divide both sides by 16 to isolate \( DE \):
\[
DE = \frac{36}{16} = \frac{9}{4} = 2.25
\]
Thus, the length of \( DE \) is \( \frac{9}{4} \) or \( 2.25 \).