Question

in triangle ABC, line PQ parallel to side BC and AP/PB=3/5 then what is AQ/QC​

Answer 1

Answer:

In triangle ABC if PQ//BC & PQ:BC = 1:3 then AP:PB = 1:2 .

Step-by-step explanation:

Given data:

In ∆ABC, PQ//BC and PQ:BC = 1:3

To find:

AP:PB

Solution:

In ∆APQ and ∆ABC, we have

∠A = ∠A ….. [common angles to both the triangles]

∠APQ = ∠ABC ……. [corresponding angles since PQ is given parallel to BC]

∴ By AA similarity, ∆APQ ~ ∆ABC

Since we know that the corresponding sides of two similar triangles are proportional to each other, so, we have

=  

⇒   = 1/3 …… [ = 1:3 given and AB = AP+PB]

⇒ 3AP = AP + PB

⇒ 3AP – AP = PB  

⇒ 2AP = PB

⇒  = ½

⇒ AP : PB = 1 : 2

Thus, the ratio of AP and PB is 1 : 2.

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