Question

In the figure above $AC=4cm,PR=2.5cm$ and $QR=4cm$. If $\overline{AB}\parallel \overline{PQ},\overline{BC}\parallel \overline{QR},\overline{AC}\parallel \overline{PR}$ and $\overline{QE}\parallel RF$ then find the length of $BE+FC$.

• A. $2.4cm$
• B. $3.6cm$
• C. $4.8cm$
• D. $6cm$

Answer 1

The correct option is A $2.4cm$

$△ABC$ and $△QRP$ are similar.

Therefore the corresponding sides are parallel.

Given, $AC=4cm,PR=2.5cm,QR=4cm$

$\frac{BC}{QR}=\frac{AC}{PR}$

$BC=\frac{4\times 4}{2.5}=6.4cm$

From Fig,

$BC=BE+EF+FC$

$BE+FC=BC-EF$

$EF=QR$

$\therefore BE+FC=BC-QR$

$BE+FC=6.4-4=2.4cm$.