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ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE is equal to :
- a)1.4 cm
- b)1.8 cm
- c)1.2 cm
- d)1.05 cm
Correct answer is option 'A'. Can you explain this answer?
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Given:
- ABC is a triangle
- DE is drawn parallel to BC, cutting the other sides at D and E
- AB = 3.6 cm
- AC = 2.4 cm
- AD = 2.1 cm
To find:
- AE
Explanation:
To find AE, we need to find the length of DE first.
Step 1: Finding the length of DE
Since DE is parallel to BC, we can use the concept of similar triangles to find its length.
Step 1.1: Establishing similarity
Triangle ABC and triangle ADE are similar by the AA similarity criterion.
Step 1.2: Writing the similarity ratio
Using the similarity ratio, we can write:
AB/AE = AC/AD
Substituting the given values:
3.6/AE = 2.4/2.1
Step 1.3: Solving for AE
Cross-multiplying, we get:
3.6 * 2.1 = 2.4 * AE
7.56 = 2.4 * AE
Dividing both sides by 2.4, we get:
AE = 7.56 / 2.4
AE ≈ 3.15 cm
Step 2: Finding AE
Now that we know the length of DE is approximately 3.15 cm, we can find AE by subtracting the length of AD from DE.
AE = DE - AD
AE = 3.15 - 2.1
AE ≈ 1.05 cm
Therefore, the value of AE is approximately 1.05 cm.
Conclusion:
The length of AE is approximately 1.05 cm, which corresponds to option 'D'.
- ABC is a triangle
- DE is drawn parallel to BC, cutting the other sides at D and E
- AB = 3.6 cm
- AC = 2.4 cm
- AD = 2.1 cm
To find:
- AE
Explanation:
To find AE, we need to find the length of DE first.
Step 1: Finding the length of DE
Since DE is parallel to BC, we can use the concept of similar triangles to find its length.
Step 1.1: Establishing similarity
Triangle ABC and triangle ADE are similar by the AA similarity criterion.
Step 1.2: Writing the similarity ratio
Using the similarity ratio, we can write:
AB/AE = AC/AD
Substituting the given values:
3.6/AE = 2.4/2.1
Step 1.3: Solving for AE
Cross-multiplying, we get:
3.6 * 2.1 = 2.4 * AE
7.56 = 2.4 * AE
Dividing both sides by 2.4, we get:
AE = 7.56 / 2.4
AE ≈ 3.15 cm
Step 2: Finding AE
Now that we know the length of DE is approximately 3.15 cm, we can find AE by subtracting the length of AD from DE.
AE = DE - AD
AE = 3.15 - 2.1
AE ≈ 1.05 cm
Therefore, the value of AE is approximately 1.05 cm.
Conclusion:
The length of AE is approximately 1.05 cm, which corresponds to option 'D'.
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ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC= 2.4 cm and AD = 2.1 cm, then AE is equal to :a)1.4 cmb)1.8cmc)1.2cmd)1.05cmCorrect answer is option 'A'. Can you explain this answer? 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 ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC= 2.4 cm and AD = 2.1 cm, then AE is equal to :a)1.4 cmb)1.8cmc)1.2cmd)1.05cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC= 2.4 cm and AD = 2.1 cm, then AE is equal to :a)1.4 cmb)1.8cmc)1.2cmd)1.05cmCorrect answer is option 'A'. Can you explain this answer?.
ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC= 2.4 cm and AD = 2.1 cm, then AE is equal to :a)1.4 cmb)1.8cmc)1.2cmd)1.05cmCorrect answer is option 'A'. Can you explain this answer? 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 ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC= 2.4 cm and AD = 2.1 cm, then AE is equal to :a)1.4 cmb)1.8cmc)1.2cmd)1.05cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a triangle and DE is drawn parallel to BC cutting the other sides at D and E. If AB = 3.6 cm, AC= 2.4 cm and AD = 2.1 cm, then AE is equal to :a)1.4 cmb)1.8cmc)1.2cmd)1.05cmCorrect answer is option 'A'. Can you explain this answer?.
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