ad=3.6 ab=10 ae=1.8 then length of ac to make DE parallel to BC is
Answers
Step-by-step explanation:
Given :-
DE||BC , AD = 3.6 units ,AB = 10 units
and AE = 1.8 units
To find :-
Find the length of AC ?
Solution :-
Given that
In ∆ ABC , DE || BC
AD = 3.6 units
AB = 10 units
AE = 1.8 units
By Basic Proportionality Theorem
AD / DB = AE /EC
On adding 1 both sides then
=> (AD/DB) +1 = (AE/EC)+1
=> (AD+DB)/DB = (AE+EC)/EC
=>AB/DB = AC/EC
=> AB/(AB-AD) = AC/(AC-AE)
=> 10/(10-3.6) = AC/(AC-1.8)
=> 10/6.4 = AC/(AC-1.8)
On applying cross multiplication then
=> 10(AC-1.8) = 6.4×AC
=> 10 AC -18 = 6.4 AC
=> 10AC -6.4 AC = 18
=> 3.6 AC = 18
=> AC = 18/3.6
=> AC = 18/(36/10)
=> AC = (18×10)/36
=> AC = 180/36
=> AC = 5
Therefore, AC = 5 units
Answer:-
The length of AC for the given problem is 5 units
Used formulae:-
Basic Proportionality Theorem:-
A line drawn parallel to one side of a triangle intersecting other two sides at two different points and the other two sides are divided into same ratio.
This is also known as Thales Theorem.
