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If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, then
- a)XY : YS = 1 : 1
- b)XY : YS = 1 : 2
- c)XY : YS = 2 : 1
- d)XY : YS = 3 : 2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If XYZ is an equilateral triangle and S is a point on YZ such that XS ...
As we know, in an equilateral triangle all sides are equal.
∴ XY = YZ = ZX
Let XY = 2a units
∴ YZ = ZX = 2a units
And XS is perpendicular bisector of side YZ
∴ YS = SZ = a units
Thus, XY: YS = 2: 1
∴ XY = YZ = ZX
Let XY = 2a units
∴ YZ = ZX = 2a units
And XS is perpendicular bisector of side YZ
∴ YS = SZ = a units
Thus, XY: YS = 2: 1
Most Upvoted Answer
If XYZ is an equilateral triangle and S is a point on YZ such that XS ...
Given information:
- XYZ is an equilateral triangle
- S is a point on YZ such that XS is perpendicular to YZ
Explanation:
Properties of an equilateral triangle:
- In an equilateral triangle, all three sides are equal in length.
- The altitude drawn from a vertex of an equilateral triangle will bisect the opposite side.
Relationship between XY and YS:
- Let's consider the equilateral triangle XYZ.
- Since XS is perpendicular to YZ, it divides YZ into two equal parts.
- Therefore, YS = SZ.
Ratio of XY to YS:
- In an equilateral triangle, the altitude (XS) divides the triangle into two 30-60-90 right-angled triangles.
- In a 30-60-90 triangle, the ratio of the sides opposite the angles is 1 : √3 : 2.
- Since YS = SZ, the ratio of XY to YS is 2 : 1.
Conclusion:
- Therefore, in the given equilateral triangle XYZ with point S on YZ such that XS is perpendicular to YZ, the ratio of XY to YS is 2 : 1. Hence, option C is correct.
- XYZ is an equilateral triangle
- S is a point on YZ such that XS is perpendicular to YZ
Explanation:
Properties of an equilateral triangle:
- In an equilateral triangle, all three sides are equal in length.
- The altitude drawn from a vertex of an equilateral triangle will bisect the opposite side.
Relationship between XY and YS:
- Let's consider the equilateral triangle XYZ.
- Since XS is perpendicular to YZ, it divides YZ into two equal parts.
- Therefore, YS = SZ.
Ratio of XY to YS:
- In an equilateral triangle, the altitude (XS) divides the triangle into two 30-60-90 right-angled triangles.
- In a 30-60-90 triangle, the ratio of the sides opposite the angles is 1 : √3 : 2.
- Since YS = SZ, the ratio of XY to YS is 2 : 1.
Conclusion:
- Therefore, in the given equilateral triangle XYZ with point S on YZ such that XS is perpendicular to YZ, the ratio of XY to YS is 2 : 1. Hence, option C is correct.
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If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer?
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If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. 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 If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer?.
If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. 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 If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer?.
Solutions for If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
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If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If XYZ is an equilateral triangle and S is a point on YZ such that XS ⊥ YZ, thena)XY : YS = 1 : 1b)XY : YS = 1 : 2c)XY : YS = 2 : 1d)XY : YS = 3 : 2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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