Question

A $△ABC$ with $AB=3$ cm, $BC=6$ cm and $AC=4$ cm is enlarged to $△DEF$ such that the longest side of $△DEF=9$ cm. Find the scale factor and hence, the lengths of the other sides of $△DEF$

Answer 1

$△ABC$ is enlarged to $△DEF$.So the two triangles will be similar.

$\therefore \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Longest side in $△ABC$ is $BC=6$cm

Corresponding longest side in $△DEF$ is $EF=9$cm

Scale factor$=\frac{EF}{BC}=\frac{9}{6}=1.5$

$\therefore \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{2}{3}$

$\Rightarrow DE=\frac{3}{2}AB=\frac{9}{2}=4.5$cm

$\Rightarrow DF=\frac{3}{2}AC=\frac{12}{2}=6$cm