Question

$△ABD\sim △DEF$ and the perimeters of $△ABC$ and $△DEF$ are $30cm$ and $18cm$ respectively. If $BC=9cm$, calculate measure of $EF$.

• A. $6.3cm$
• B. $5.4cm$
• C. $7.2cm$
• D. $4.5cm$

Answer 1

The correct option is B $5.4cm$

Similar triangles are triangle with similar shape but can have different sizes.

Since there is something common about them, then to establish the relationship we have something called linear scale factor which is used to get the length of the other when the length of the other similar triangles is known.

$LSF=\frac{30}{18}=\frac{5}{3}$

$\frac{BC}{EF}=\frac{5}{3}\Rightarrow \frac{9}{EF}=\frac{5}{3}$

$\therefore EF=9\times \frac{3}{5}=5.4cm$