SSC Exam > SSC Questions > In ∆ABC, AB = 12 cm, BC = 10 cm and AC ...
Start Learning for Free
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.
- a)8 cm
- b)7 cm
- c)10 cm
- d)11 cm
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approxim...
As per the given data
Let AD be the length of the median subtending from vertex A and to the side BC
⇒ BD = DC = BC/2 = 10/2 = 5 cm
By Apollonius theorem, we get
⇒ AB2 + AC2 = 2 (AD2 + BD2)
⇒ 122 + 62 = 2 (AD2 + 52)
⇒ 90 = AD2 + 25
⇒ 65 = AD2
⇒ AD = 8.06 cm
∴ length of the medium = AD = 8.06 ≈ 8 cm
Let AD be the length of the median subtending from vertex A and to the side BC
⇒ BD = DC = BC/2 = 10/2 = 5 cm
By Apollonius theorem, we get
⇒ AB2 + AC2 = 2 (AD2 + BD2)
⇒ 122 + 62 = 2 (AD2 + 52)
⇒ 90 = AD2 + 25
⇒ 65 = AD2
⇒ AD = 8.06 cm
∴ length of the medium = AD = 8.06 ≈ 8 cm
Most Upvoted Answer
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approxim...
Given: AB = 12 cm, BC = 10 cm and AC = 6 cm
To find: Approximate length of median from vertex A
Median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Let's assume D as the midpoint of BC.
Steps:
1. Find the value of BD and DC using the formula of midpoint. BD = DC = BC/2 = 10/2 = 5 cm
2. Using the Pythagorean theorem, find the value of AD.
AD^2 = AB^2 - BD^2
= 12^2 - 5^2
= 119
AD = √119 ≈ 10.9 cm
3. The median from vertex A divides the side BC into two equal parts.
Therefore, the length of BM = MC = BC/2 = 5 cm
4. Using the Pythagorean theorem, find the value of AM.
AM^2 = AD^2 - DM^2
= 119 - 5^2
= 94
AM = √94 ≈ 9.7 cm
5. The approximate length of the median from vertex A is the average of BM and AM.
Median from vertex A ≈ (BM + AM)/2
= (5 + 9.7)/2
= 7.35 ≈ 8 cm
Therefore, the approximate length of the median from vertex A is 8 cm, which is option (a)
To find: Approximate length of median from vertex A
Median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Let's assume D as the midpoint of BC.
Steps:
1. Find the value of BD and DC using the formula of midpoint. BD = DC = BC/2 = 10/2 = 5 cm
2. Using the Pythagorean theorem, find the value of AD.
AD^2 = AB^2 - BD^2
= 12^2 - 5^2
= 119
AD = √119 ≈ 10.9 cm
3. The median from vertex A divides the side BC into two equal parts.
Therefore, the length of BM = MC = BC/2 = 5 cm
4. Using the Pythagorean theorem, find the value of AM.
AM^2 = AD^2 - DM^2
= 119 - 5^2
= 94
AM = √94 ≈ 9.7 cm
5. The approximate length of the median from vertex A is the average of BM and AM.
Median from vertex A ≈ (BM + AM)/2
= (5 + 9.7)/2
= 7.35 ≈ 8 cm
Therefore, the approximate length of the median from vertex A is 8 cm, which is option (a)
|
Explore Courses for SSC exam
|
|
Similar SSC Doubts
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer?
Question Description
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer?.
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer?.
Solutions for In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
Download more important topics, notes, lectures and mock test series for SSC Exam by signing up for free.
Here you can find the meaning of In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In ∆ABC, AB = 12 cm, BC = 10 cm and AC = 6 cm. Find the approximate length of the median from vertex A.a)8 cmb)7 cmc)10 cmd)11 cmCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice SSC tests.
|
|
Explore Courses for SSC 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup