In ∆ABC, DE || BC
If DB = 5.4 cm, AD = 1.8 cm
EC = 7.2 cm then find AE.
Answers
Step-by-step explanation:
In triangle ABC,
DE║BC
DB = 5.4 cm
AD = 1.8 cm
EC = 7.2 cm
To be found:
The value of AE?
Now,
[see the attached image]
We know that,
BPT - Basic Proportionality Theorem.
When a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
Another name of it is - Thales theorem.
So,
We get
\boxed{\frac{AD}{BD}=\frac{AE}{CE}}
BD
AD
=
CE
AE
So,
Putting the given values in the above, we will get,
\implies \frac{1.8}{5.4}=\frac{AE}{7.2}⟹
5.4
1.8
=
7.2
AE
By cross multiplication, we will get,
⇒ 7.2 * 1.8 = 5.4 * AE
⇒ 12.97 = 5.4 * AE
⇒ 12.97 ÷ 5.4 = AE
⇒ 2.4 = AE
Hence,
The value of Ae is 2.4 cm
- - -
Verification,
\boxed{\frac{AD}{BD}=\frac{AE}{CE}}
BD
AD
=
CE
AE
LHS,
\frac{AD}{BD}= \frac{1.8}{5.4} = 0.33
BD
AD
=
5.4
1.8
=0.33
RHS,
=\frac{AE}{CE} = \frac{2.4}{7.2} = 0.33=
CE
AE
=
7.2
2.4
=0.33
Hence,
LHS = RHS (verified)
