Question

Triangle ABC is similar to Triangle DEF. if the length of AB is 2 cm, DE is 10 cm, and BC is 7cm what is the length of EF in cm?

Answer 1

Since triangle ABC is similar to triangle DEF, the ratios of the corresponding sides are equal.

Given:
- Length of AB = 2 cm
- Length of DE = 10 cm
- Length of BC = 7 cm
- We need to find the length of EF.

First, we can set up a ratio using sides AB and DE:

\[
\frac{AB}{DE} = \frac{BC}{EF}
\]

Substituting the known values:

\[
\frac{2}{10} = \frac{7}{EF}
\]

This can be simplified:

\[
\frac{1}{5} = \frac{7}{EF}
\]

Now, we can cross-multiply to find EF:

\[
1 \cdot EF = 5 \cdot 7
\]

\[
EF = 35
\]

Thus, the length of EF is \( \boxed{35} \) cm.