In ∆ABC , D and E are points
AB and BC respectively such that
DE II BC, If AD=1/3 BD, AE = 4.5 cm
find AC.
Answers
Answer:
My best answer is, AC = 13.5 cm
I hope it will help you.
Answer :
Given :-
In ∆ABC , D and E are points AB and BC respectively such that DE II BC and AD=1/3 BD, AE = 4.5 cm.
To find :-
Find AC ?
Solution :-
Given that:
In ∆ABC , D and E are points AB and BC respectively such that DE II BC.
AD=1/3 BD
=> AD / DB = 1/3 ------(1)
AE = 4.5 cm.----(2)
We know that by Thales Theorem
=> AD / DB = AE / EC
From (1) &(2)
=> 1/3 = 4.5/ EC
On applying cross multiplication then
=> EC × 1 = 3×4.5
=> EC = 13.5 cm
Therefore, EC = 13.5 cm
But AC = AE+EC
AC = 4.5 + 13.5
=> AC = 18.0
=> AC = 18 cm
Therefore, AC = 18 cm
Answer:-
The value of AC for the given problem is 18 cm
Used Theorem :-
Thales Theorem :-
A line drawn parallel to one sides of a triangle Intersecting other two sides at different points and the two sides are divided into equal ratio.
- This is known as Basic Proportionality Theorem .