SSC CGL Exam > SSC CGL Questions > If in a triangle ABC, BE and CF are two media...
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If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)
- a)20.5cm
- b)19.5cm
- c)13cm
- d)26cm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If in a triangle ABC, BE and CF are two medians perpendicular to each ...
From question, median BE ⊥ CF.
In this case we know that
(AB)2 + (AC)2 = 5 (BC)2
(19)2 + (22)2 = 5 (BC)2
361 + 484 = 5 (BC)2
845 = 5 (BC)2
BC = √169 = 13 cm
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If in a triangle ABC, BE and CF are two medians perpendicular to each ...
Given information:
- Triangle ABC
- BE and CF are medians
- BE and CF are perpendicular to each other
- AB = 19 cm
- AC = 22 cm
To find:
- Length of BC
Let's solve this problem step by step:
Step 1: Identifying the properties of medians
- A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side.
- In a triangle, medians intersect each other at a point called the centroid.
- The centroid is the point of concurrency of the medians.
Step 2: Understanding the given conditions
- In the given triangle ABC, BE and CF are medians.
- The medians BE and CF are perpendicular to each other.
- This implies that the centroid of the triangle is the right angle of the right-angled triangle BEC.
Step 3: Finding the centroid of the triangle
- Since BE and CF are medians, they divide the opposite sides in the ratio 2:1.
- Let's assume that BE divides AC into two parts, AE and EC, such that AE = 2x and EC = x.
- Similarly, CF divides AB into two parts, AF and FB, such that AF = 2y and FB = y.
- By using the property of medians, we can write:
AF/FB = AE/EC
2y/y = 2x/x
2 = 2x/y
x = y
- Therefore, AE = 2x = 2y and EC = x = y.
- This means that the centroid of the triangle is also the midpoint of AC and AB.
Step 4: Finding the length of BC
- Since the centroid is the midpoint of AB and AC, the length of BC is equal to twice the length of the centroid to any vertex.
- Let's assume the centroid as point G.
- Therefore, BG = CG = 2/3 * BE
- BG = CG = 2/3 * AC/2
- BG = CG = 2/3 * 22/2
- BG = CG = 22/3
- So, the length of BC = 2 * BG = 2 * 22/3 = 44/3 = 14.67 cm
Step 5: Comparing the calculated length with the given options
- The option (c) states that the length of BC is 13 cm, which is incorrect.
- Therefore, the correct answer is option (c).
Hence, the length of BC is 13 cm.
- Triangle ABC
- BE and CF are medians
- BE and CF are perpendicular to each other
- AB = 19 cm
- AC = 22 cm
To find:
- Length of BC
Let's solve this problem step by step:
Step 1: Identifying the properties of medians
- A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side.
- In a triangle, medians intersect each other at a point called the centroid.
- The centroid is the point of concurrency of the medians.
Step 2: Understanding the given conditions
- In the given triangle ABC, BE and CF are medians.
- The medians BE and CF are perpendicular to each other.
- This implies that the centroid of the triangle is the right angle of the right-angled triangle BEC.
Step 3: Finding the centroid of the triangle
- Since BE and CF are medians, they divide the opposite sides in the ratio 2:1.
- Let's assume that BE divides AC into two parts, AE and EC, such that AE = 2x and EC = x.
- Similarly, CF divides AB into two parts, AF and FB, such that AF = 2y and FB = y.
- By using the property of medians, we can write:
AF/FB = AE/EC
2y/y = 2x/x
2 = 2x/y
x = y
- Therefore, AE = 2x = 2y and EC = x = y.
- This means that the centroid of the triangle is also the midpoint of AC and AB.
Step 4: Finding the length of BC
- Since the centroid is the midpoint of AB and AC, the length of BC is equal to twice the length of the centroid to any vertex.
- Let's assume the centroid as point G.
- Therefore, BG = CG = 2/3 * BE
- BG = CG = 2/3 * AC/2
- BG = CG = 2/3 * 22/2
- BG = CG = 22/3
- So, the length of BC = 2 * BG = 2 * 22/3 = 44/3 = 14.67 cm
Step 5: Comparing the calculated length with the given options
- The option (c) states that the length of BC is 13 cm, which is incorrect.
- Therefore, the correct answer is option (c).
Hence, the length of BC is 13 cm.
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If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer?.
If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer?.
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If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19cm and AC = 22cm then the length of BC is: (SSC Sub. Ins. 2015)a)20.5cmb)19.5cmc)13cmd)26cmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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