Question

P and q are points on the sides AB and AC respectively of triangle ABC such that AP = 3.5 cm, PB =7cm, AQ = 3cm and QC = 6 cm. If PQ = 4•5 cm , find BC

Answer 1

bc = 9 cm using similarity theorem

Answer 2

The length of side BC is 9 cm

GIVEN

ABC is a triangle.

AP = 3.5cm

PB = 7cm

AQ = 3cm

QC = 6cm.

TO FIND

The length of BC.

SOLUTION

We can simply solve the above problem as follows-

In ∆ABC and ∆APQ

∠BAC = ∠PAQ (Common angle)

And, QP // BC

∠AQP = ∠ACB (Corresponding angle)

Therefore,

ΔABC ≈ AQP ( By ASA criterion)

Applying the thales intercept theoram

AQ/QC = QP/BC

Putting the values of AQ, QC, QP

3/6 = 4.5/BC

BC = 4.5×6/3

BC = 9cm

Hence, The length of side BC is 9 cm

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