Question
If $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are similar triangles such that AB = 3cm, BC = 2cm, CA = 2.5cm and EF = 4cm, write the perimeter of $\triangle\text{DEF}.$
✓
Answer
$\because\triangle\text{ABC}\sim\triangle\text{DEF}$
$\therefore\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}$
But AB = 3cm, BC = 2cm, CA = 2.5cm and EF = 4cm.
$\therefore\frac{3}{\text{DE}}=\frac{2}{4}=\frac{2.5}{\text{FD}}$
Now $\frac{3}{\text{DE}}=\frac{2}{4}\Rightarrow\text{DE}=\frac{3\times4}{2}=6\text{cm}$
and $\frac{\text{CA}}{\text{FD}}=\frac{2}{4}\Rightarrow\frac{2.5}{\text{FD}}=\frac{2}{4}$
$\text{FD}=\frac{2.5\times4}{2}=5\text{cm}$
$\therefore$ Perimeter of $\triangle\text{DEF}=6+4+5=15\text{cm}$
$\therefore\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}$
But AB = 3cm, BC = 2cm, CA = 2.5cm and EF = 4cm.
$\therefore\frac{3}{\text{DE}}=\frac{2}{4}=\frac{2.5}{\text{FD}}$
Now $\frac{3}{\text{DE}}=\frac{2}{4}\Rightarrow\text{DE}=\frac{3\times4}{2}=6\text{cm}$
and $\frac{\text{CA}}{\text{FD}}=\frac{2}{4}\Rightarrow\frac{2.5}{\text{FD}}=\frac{2}{4}$
$\text{FD}=\frac{2.5\times4}{2}=5\text{cm}$
$\therefore$ Perimeter of $\triangle\text{DEF}=6+4+5=15\text{cm}$
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