Question

In the given figure, $AB\parallel DC$, BO = 6 cm and DO = 8 cm; find $BP\times DO$

• A. $42{\text{cm}}^2$
• B. $46{\text{cm}}^2$
• C. $48{\text{cm}}^2$
• D. $52{\text{cm}}^2$

Answer 1

The correct option is C

$48{\text{cm}}^2$

In the given figure,

$AB\parallel DC$,

BO = 6 cm, DO = 8 cm

In $\Delta ODQ$ and $\Delta OPB$

$\angle DOQ=\angle POB$ (Vertically opposite angles)

$\angle DQO=\angle OPB$ (Alternate angles)

$\therefore \Delta ODQ\sim \Delta OPB$

$\therefore \frac{DQ}{PB}=\frac{QO}{OP}=\frac{DO}{OB}$

$\Rightarrow \frac{8}{PB}=\frac{DO}{6}$

By cross multiplication,

$PB\times DO=8\times 6=48{\text{cm}}^2$