Question

Triangle ABC is similar to Triangle DEF. If the length of AB is 2cm , 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 corresponding sides of the triangles are proportional.

We can set up the following proportion based on the sides AB and DE:

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

Substituting the known lengths into the proportion:

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

Now, we can simplify the left side:

\[
\frac{2}{10} = \frac{1}{5}
\]

So we have:

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

Now, we can cross-multiply to solve for EF:

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

\[
EF = 35
\]

Therefore, the length of EF is \( 35 \) cm.