Question

In Fig. 4.137,AB||QR . Find the length of PB.

Answer 1

Answer:

as per figure..

in APB and QPR

from theorem...

AB/QR= PB/PR= PA/PQ

3/9= PB/6

9PB= 6×3

PB= 18/9

PB = 2

Answer 2

Given : AB || QR, AB = 3 cm, QR = 9 cm and PR = 6 cm

To find : length of PB.

Solution :

In ∆ PAB & ∆PQR

∠PAB = ∠PQR and ∠PBA = ∠PRQ   [Corresponding angles]

∠P = ∠P   [Common]

∆PAB ∼ ∆PQR

[By AAA similarity criterion]

AB/QR = PB/PR

[Since, triangles are similar , hence corresponding sides will be proportional]

3/9 = PB/6

3 × 6 = 9 PB

PB = (3 × 6)/9

PB = 6/3

PB = 2 cm

Hence, the value of PB = 2 cm.

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