If ΔABC is similar to ΔDEF , and AB= 16, DF= 3, and AC= 12, what is the length of DE ? (1 point) Responses 2.25 2.25 64 64 7 7 4

Answer 1

Since triangles ΔABC and ΔDEF are similar, their corresponding sides are in proportion.

Given that:

• AB corresponds to DF,
• AC corresponds to DE.

We can set up the proportion based on the lengths of sides AB and DF:

\[ \frac{AB}{DF} = \frac{AC}{DE} \]

Substituting the known values:

\[ \frac{16}{3} = \frac{12}{DE} \]

Next, we can cross-multiply to solve for DE:

\[ 16 \cdot DE = 12 \cdot 3 \]

Calculating the right side:

\[ 16 \cdot DE = 36 \]

Now, we divide both sides by 16 to isolate DE:

\[ DE = \frac{36}{16} = \frac{9}{4} = 2.25 \]

Therefore, the length of DE is 2.25.