Question

Angles BAC of triangle ABC is obtuse and AB = AC. P is a point in BC such that PC = 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively.

If PQ = 15 cm and PR = 9 cm; then the length of PB is ___ cm.

Answer 1

In $\Delta ABC$, $\angle BAC$ is an obtuse angle and AB = AC.

P is a point on BC such that PC = 12 cm

PQ and PR are perpendiculars to the sides AB and AC respectively.

PQ = 15 cm and PR = 9 cm

To find the length of PB

In $\Delta PBQ$ and $\Delta PCR$

$\angle PBQ=\angle PCR$ (Opposite angles of equal sides)

$\angle PQB=\angle PRC$ (Each ${90}^{\circ }$)

$\therefore \Delta PBQ\sim \Delta PCR$ (AA axiom)

$\therefore \frac{PB}{PC}=\frac{PQ}{PR}$ (corresponding sides are proportional)

$\Rightarrow \frac{x}{12}=\frac{15}{9}\Rightarrow x=\frac{15\times 12}{9}=20$

$\therefore$ PB = 20 cm.