Given that the triangles are similar, the corresponding sides of the triangles are proportional.
Let's denote the triangles as \(\triangle ABC\) and \(\triangle DEF\), where \(\triangle ABC \sim \triangle DEF\).
From the given information:
- \(DE = 9\)
- \(EF = 7\)
- \(AB = 4.5\)
We need to find the length of \(BC\) (which corresponds to \(EF\)).
Since \(\triangle ABC \sim \triangle DEF\):
\[
\frac{AB}{DE} = \frac{BC}{EF}
\]
Plugging in the values we know:
\[
\frac{4.5}{9} = \frac{BC}{7}
\]
Simplifying \(\frac{4.5}{9}\):
\[
\frac{4.5}{9} = \frac{1}{2}
\]
So,
\[
\frac{1}{2} = \frac{BC}{7}
\]
To find \(BC\), we solve for \(BC\):
\[
BC = \frac{1}{2} \times 7 = 3.5
\]
Therefore, the length of \(BC\) is \(3.5\).
The answer is:
\[
\boxed{3.5}
\]
The triangles are similar. If DE = 9, EF = 7, and AB = 4.5, find BC.
9
14
3.5
7
1 answer