Question

In ABC, P divides the side AB such that AP: PB = 1:2. Q is a point in AC
such that PQ II BC. Find the length of AQ if AC = 4.5cm.​

Answer 1

Step-by-step explanation:

Given:-

In ∆ABC, PQ is parallel to BC and AP:PB = 1:2 and AC = 4.5cm

To find:-

Find the length of AQ ?

Solution:-

Given that

In ∆ABC , PQ II BC.

Given that AP : PB = 1:2

We know that the theorem

Basic Proportionality Theorem :-

"A line drawn Parallel to one side of a triangle divides the remaining sides in the same ratio".

=> AP/PB =AQ/QC

=>1/2 = AQ/QC

we know that from figure

AC = AQ+QC

=> QC = AC - AQ

Now , On Substituting the value in it

=>1/2 = AQ/(AC - AQ)

and we have AC = 4.5 cm

=>1/2 = AQ /(4.5-AQ)

On applying cross multiplication then

= 2AQ = 4.5-AQ

=>2AQ+AQ = 4.5

=>3 AQ = 4.5

=>AQ = 4.5/3

=>AQ = 1.5 cm

Therefore,AQ = 1.5 cm

Answer:-

The length of the AQ = 1.5 cm

Used formula:-

.Basic Proportionality Theorem or Thales Theorem:-

• A line drawn Parallel to one side of a triangle and it touches the remaining sides in two different points and they are divided in the same ratio or they are in proportion.