in ∆ABC, DE || BC, if DB = 1.8 cm, AD = 5.4 cm, AE = 7.2 cm then find EC.
Answers
Answer:
Answer:
Given:
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
AD AE
BD
So,
CE
Putting the given values in the above, we will get,
1.8 5.4
AE 7.2
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,
AD
AE CE BD
LHS,
AD BD 1.8 5.4 = 0.33
RHS,
= AE CE 2.4 7.2 = 0.33
Hence,
LHS = RHS (verified)
RHS,
AE
CE
Hence,
LHS = RHS (verified)
=2.4=7.2=0.33
Step-by-step explanation:
Hope this answer will help you.