Question

In the figure, Pg is drawn parallel to
PQ : BC = 1:3. the ratio of AP and
BC of the AABC.
e)
If
base
2.
PB will be
​

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

\frac{AP}{AB}

AB

AP

= \frac{PQ}{BC}

BC

PQ

⇒ \frac{AP}{AP+PB}

AP+PB

AP

= 1/3 …… [\frac{PQ}{BC}

BC

PQ

= 1:3 given and AB = AP+PB]

⇒ 3AP = AP + PB

⇒ 3AP – AP = PB

⇒ 2AP = PB

⇒ \frac{AP}{PB}

PB

AP

= ½

⇒ AP : PB = 1 : 2

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

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Learn More:

If areas of 2 similar triangles are equal prove that they are congruent

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Proof of the theorem: ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

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Answer 2

Hope above of my answer's will be helpful to you...........