Question

In $△ABC,E$ and $F$ are the midpoints of the sides $AB$ and $AC$ respectively. In $△AEF,G$ and $H$ are midpoints of the sides $AE$ and $AF$ respectively. If $GH=1.8cm$, find $BC$

• A. $0.9cm$
• B. $3.6cm$
• C. $7.2cm$
• D. $5.4cm$

Answer 1

Answer: (C)

$7.2cm$

In $\Delta ABC$ and $\Delta AGH$

$\frac{AG}{AB}=\frac{AH}{AC}=\frac{1}{4}$

$\angle A$ (common)

$\angle AGH=\angle ABC$

$\therefore \Delta ABC\approx \Delta AGH$

$\Rightarrow \frac{AG}{AB}=\frac{AH}{AC}=\frac{GH}{BC}=\frac{1}{4}$

$\Rightarrow BC=4\times GH=4\times 1.8=7.2cm$

$\Rightarrow BC=7.2cm$