Question

In the figure, PQ//BC, IF PQ/BC=2/5, THEN AP/PB

Answer 1

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Answer 2

Given:

PQ||BC and PQ/BC = 2/5.

To find:

AP/PB =?

Solution:

As we know that if two lines are parallel then their corresponding angles will be equal. So, as given PQ||BC, we have

angle APQ = angle ABC (i)

and

angle AQP = angle ACB (ii)

Also,

angle A = angle A (iii)

(Corresponding angles)

Hence, from (I), (ii) and (iii)

Triangle APQ is similar to triangle ABC.

Now,

As we know that if two triangles are similar then their corresponding angles will be in the same proportion.

So,

In triangle APQ and ABC, we have

$\frac{PQ}{BC} = \frac{AP}{AB}$

$\frac{2}{5} = \frac{AP}{AB}$

$\frac{AP}{AB} = \frac{2}{5}$ (iv)

Also,

AB = AP+ PB

5 = 3 + PB

PB = 5 - 3 = 2

So, after putting the value of PB in (iv), we have

$\frac{AP}{PB} = \frac{2}{3}$

Hence, AP/PB = 2/3.