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
In ΔABC, ∠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 ΔPBQ and ΔPRC
∠B=∠C (Opposite angles of equal sides)
∠Q=∠P (Each 90∘)
∴ΔPBQ∼ΔPRC (AA axiom)
∴PBPC=PQPR (corresponding sides are proportional)
⇒x12=159⇒x=15×129=20
∴ PB = 20 cm