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D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is?
Verified Answer
D and e are respectively the points on the sides ab and ac of a triang...
Given:
∆ABC in which DE // BC. AD = 2cm, BD = 3 cm and BC = 7.5 cm.
To find:
The length of DE
Since, DE is parallel to BC
→ angle ADE = angle ABC (corresponding angles)
→ angle AED = angle ACB (corresponding angles)
Hence, by AA criterion of similarity,
∆ADE ~ ∆ABC
ratio of corresponding sides of similar triangles are equal.
AD/AB = DE/BC
AB = AD + DB
AB = 2 + 3 = 5 cm
So,
2/5 = DE/7.5
DE = 2/5 x 7.5
DE = 2 x 1.5
DE = 3 cm.
Hence, the length of side DE is 3 cm.
∆ABC in which DE // BC. AD = 2cm, BD = 3 cm and BC = 7.5 cm.
To find:
The length of DE
Since, DE is parallel to BC
→ angle ADE = angle ABC (corresponding angles)
→ angle AED = angle ACB (corresponding angles)
Hence, by AA criterion of similarity,
∆ADE ~ ∆ABC
ratio of corresponding sides of similar triangles are equal.
AD/AB = DE/BC
AB = AD + DB
AB = 2 + 3 = 5 cm
So,
2/5 = DE/7.5
DE = 2/5 x 7.5
DE = 2 x 1.5
DE = 3 cm.
Hence, the length of side DE is 3 cm.
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
D and e are respectively the points on the sides ab and ac of a triang...
Understanding the Problem
In triangle ABC, we have points D and E on sides AB and AC, respectively. The key details provided are:
- AD = 3 cm
- BD = 5 cm
- BC = 12.8 cm
- DE is parallel to BC
Using the Basic Proportionality Theorem
Since DE is parallel to BC, we can apply the Basic Proportionality Theorem (also known as Thales' theorem), which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
Calculating Proportions
1. Identify Segments:
- Total length of AB: AB = AD + BD = 3 cm + 5 cm = 8 cm.
2. Determine Ratios:
- The ratio of AD to AB is: AD / AB = 3 cm / 8 cm.
- This ratio also applies to DE and BC because DE is parallel to BC.
3. Set Up the Equation:
- If DE is x cm long, then according to the theorem:
x / BC = AD / AB
- Substituting the values:
x / 12.8 cm = 3 cm / 8 cm.
Solving for DE
To find x (the length of DE), cross-multiply:
- x * 8 = 3 * 12.8
- x * 8 = 38.4
- x = 38.4 / 8
- x = 4.8 cm.
Conclusion
The length of DE is 4.8 cm. This solution demonstrates the power of proportional relationships in similar triangles, highlighting the importance of parallel lines in geometric figures.
In triangle ABC, we have points D and E on sides AB and AC, respectively. The key details provided are:
- AD = 3 cm
- BD = 5 cm
- BC = 12.8 cm
- DE is parallel to BC
Using the Basic Proportionality Theorem
Since DE is parallel to BC, we can apply the Basic Proportionality Theorem (also known as Thales' theorem), which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
Calculating Proportions
1. Identify Segments:
- Total length of AB: AB = AD + BD = 3 cm + 5 cm = 8 cm.
2. Determine Ratios:
- The ratio of AD to AB is: AD / AB = 3 cm / 8 cm.
- This ratio also applies to DE and BC because DE is parallel to BC.
3. Set Up the Equation:
- If DE is x cm long, then according to the theorem:
x / BC = AD / AB
- Substituting the values:
x / 12.8 cm = 3 cm / 8 cm.
Solving for DE
To find x (the length of DE), cross-multiply:
- x * 8 = 3 * 12.8
- x * 8 = 38.4
- x = 38.4 / 8
- x = 4.8 cm.
Conclusion
The length of DE is 4.8 cm. This solution demonstrates the power of proportional relationships in similar triangles, highlighting the importance of parallel lines in geometric figures.
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D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is?
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D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is? 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 D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is?.
D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is? 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 D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for D and e are respectively the points on the sides ab and ac of a triangle abc such that ad=3cm bd=5cm bc =12.8 cm and de is Parallel to bc . Then length of de in cm is?.
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