In the given figure, DE||BC such that AE = 1/4AC. If DE = 6 cm, then the value of BC is
(1) 20 cm
(2) 36 cm
(3) 24 cm
(4) 15 cm
Answers
Answer:
Answer
As DE∥BC
∠ADE=∠ABC
∠AED=∠ACB
So by AAA △ADE∼△ABC
Hence
AB
AD
=
AC
AE
AC
AE
=
4
1
6
AD
=
4
1
AD=1.5cm
So AD=1.5cm
Answer:
Option (3)
Step-by-step explanation:
Given :-
In the given figure, DE||BC such that
AE = 1/4AC and DE = 6 cm.
To find :-
Find the value of BC ?
Solution :-
Given that :
In the given figure, DE||BC such that
AE = 1/4AC
=> AE = (1/4) AC
=> AE / AC = 1/4
=> AE/ (AE+EC) = 1/4
=> (AE+EC)/AE = 4/1
=> (AE/AE) + (EC/AE) = 4
=> 1+(EC/AE) = 4
=> (EC/AE) = 4-1
=> (EC/AE) = 3
=> AE/EC = 1/3
We know that by Thales Theorem
AD / DB = AE / EC
=> AD/DB = 1/3
=> DB/AD = 3------(1)
and DE = 6 cm.
From ∆ ABC and ∆ABE
angle B = angle ADE
Since Corresponding angles are equal
angle A = angle A
Common angle
By AA Similar Property
∆ ABC ~ ∆ ADE
BC / DE = AB / DA
=> BC/6 = AB/AD
=> BC/6 = (AD+DB)/AD
=>BC/6 = (AD/AD)+(DB/AD)
=>BC/6 = 1+(DB/AD)
=>BC/6 = 1+3 (from (1))
=> BC /6 = 4
=> BC = 4×6 cm
=> BC = 24 cm
Therefore, BC = 24 cm
Answer:-
The value of BC for the given problem is 24 cm
Used formulae:-
1.Thales Theorem:-
A line drawn parallel to one side of a triangle , the line Intersects another two sides at different points then the other two sides are divided into same ratio. This theorem is called Thales Theorem or Basic Proportionality Theorem.
2.AA Similar Property:-
In two triangles The two angles in a triangle are equal to the corresponding angles in the second triangle then they are similar triangles. This property is called AA Similar Property .
3. If two triangles are said to be similar ,
- The corresponding angles are equal.
- The corresponding sides are in the same ratio. (in the proportion).