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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.

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Solution

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)

ΔPBQΔPRC (AA axiom)

PBPC=PQPR (corresponding sides are proportional)

x12=159x=15×129=20

PB = 20 cm


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