Question

In the given figure, AB || QR. Find the length of PB.

Answer 1

SOLUTION :  

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

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 = 9PB

PB = (3×6)/9

PB = 6/3

PB = 2 cm

Hence, the value of PB = 2 cm.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

PB= 2cm

Step-by-step explanation:

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

Required: Length of PB

In ∆ PAB & ∆PQR:

i) ∠PAB = ∠PQR and ∠PBA = ∠PRQ (Corresponding angles)

ii) ∠P = ∠P  (Common)

So, ∆PAB ∼ ∆PQR

[AA similarity]

Therefore, AB/QR = PB/PR

We know that since, triangles are similar , so the ratio of corresponding sides will be equal.

∴ 3/9 = PB/6

3 × 6 = 9PB

PB = (3×6)/9

PB = 18/9

PB = 2 cm

Hope it helps. Thanks :)