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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.?
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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.
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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.?
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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 2024 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 2024 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 2024 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 2024 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.?.
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