Question

In the given figure, $2AP=5PB$ and $2CP=5PD$

If $AC=10cm,$ then find the length of $BD$ ( in cm )

Answer 1

Given, 2 PA = 5 PB and 2 CP = 5 PD

hence, $\frac{PA}{PB}=\frac{5}{2}$ and $\frac{PC}{PD}=\frac{5}{2}$

Now, in $△$s, PAC and PDB,

$\angle APC=\angle BPD$ (Vertically opposite angles)

$\frac{PA}{PB}=\frac{PC}{PD}$

Thus, $△APC\sim △BPD$ (SAS rule)

Thus, $\frac{PA}{PB}=\frac{AC}{BD}$

$\frac{5}{2}=\frac{10}{BD}$

$BD=\frac{10\times 2}{5}$

$BD=4cm$