Class 10 Exam > Class 10 Questions > If D and E are point on the side AD of triang...
Start Learning for Free
If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.?
Most Upvoted Answer
If D and E are point on the side AD of triangle ABC such that AB = 5.6...
Given information:
- AB = 5.6 cm
- AD = 1.4 cm
- AC = 7.2 cm
- AE = 1.8 cm
- DE // BC
Explanation:
Using Similarity of Triangles:
1. Since DE is parallel to BC, we can use the concept of similar triangles to find the length of DE.
2. By the similarity criterion, we have triangles ADE and ABC similar.
3. Therefore, we can set up a proportion based on the corresponding sides of the two triangles.
Calculating the Length of DE:
- In triangle ADE and ABC:
- AD/AB = AE/AC (By the similarity of triangles)
- 1.4/5.6 = 1.8/7.2
- 1/4 = 1/4
- This shows that the triangles are similar.
- Now, we can use this similarity to find the length of DE:
- DE/BC = AE/AC
- DE/BC = 1.8/7.2
- DE/BC = 1/4
- DE = BC/4
- Since BC = AB - AC = 5.6 - 7.2 = -1.6 cm
- DE = -1.6/4 = -0.4 cm
Conclusion:
- The length of DE is -0.4 cm. This negative length indicates that the direction of DE is opposite to that of BC.
- Therefore, the length of DE is 0.4 cm in the opposite direction of BC to maintain the parallelism between DE and BC.
- AB = 5.6 cm
- AD = 1.4 cm
- AC = 7.2 cm
- AE = 1.8 cm
- DE // BC
Explanation:
Using Similarity of Triangles:
1. Since DE is parallel to BC, we can use the concept of similar triangles to find the length of DE.
2. By the similarity criterion, we have triangles ADE and ABC similar.
3. Therefore, we can set up a proportion based on the corresponding sides of the two triangles.
Calculating the Length of DE:
- In triangle ADE and ABC:
- AD/AB = AE/AC (By the similarity of triangles)
- 1.4/5.6 = 1.8/7.2
- 1/4 = 1/4
- This shows that the triangles are similar.
- Now, we can use this similarity to find the length of DE:
- DE/BC = AE/AC
- DE/BC = 1.8/7.2
- DE/BC = 1/4
- DE = BC/4
- Since BC = AB - AC = 5.6 - 7.2 = -1.6 cm
- DE = -1.6/4 = -0.4 cm
Conclusion:
- The length of DE is -0.4 cm. This negative length indicates that the direction of DE is opposite to that of BC.
- Therefore, the length of DE is 0.4 cm in the opposite direction of BC to maintain the parallelism between DE and BC.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.?
Question Description
If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.?.
If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.?.
Solutions for If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? defined & explained in the simplest way possible. Besides giving the explanation of
If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.?, a detailed solution for If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? has been provided alongside types of If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? theory, EduRev gives you an
ample number of questions to practice If D and E are point on the side AD of triangle ABC such that AB = 5.6 cm , AD =1.4 cm , AC = 7.2 cm , and AE = 1.8 cm , so that DE // BC.? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup