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In the given figure, ABCD is a rhombus in which ∠C = 60°. Then, find the value of AC : BD.
- a)√3 : 4
- b)4 : √3
- c)√3 : 2
- d)√3 : 1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In the given figure, ABCD is a rhombus in which∠C = 60°. Then,...
Given:-
∠C = 60°
Calculation:-
∵ ABCD is a rhombus, So, its all sides are equal.
∴ BC = DC
⇒ ∠BDC = ∠DBC = x°
In Δ BCD,
⇒ x° + x° + 60° = 180°
⇒ 2x = 120
⇒ x = 60°
∵ ∠BDC = ∠DBC = ∠DCB = 60°
∴ BD = BC = CD
Let BD = BC = CD = a,
In right angle Δ AOB,
AB2 = OA2 + OB2
OA2 = AB2 - OB2
OA2 = a2 - (a/2)2
OA2 = 3a2/4
OA = √3a/2
∵ AC = 2 × OA
AC = √3a
∴ AC : BD = √3a : a
AC : BD = √3 : 1
Community Answer
In the given figure, ABCD is a rhombus in which∠C = 60°. Then,...
Given:-
∠C = 60°
Calculation:-
∵ ABCD is a rhombus, So, its all sides are equal.
∴ BC = DC
⇒ ∠BDC = ∠DBC = x°
In Δ BCD,
⇒ x° + x° + 60° = 180°
⇒ 2x = 120
⇒ x = 60°
∵ ∠BDC = ∠DBC = ∠DCB = 60°
∴ BD = BC = CD
Let BD = BC = CD = a,
In right angle Δ AOB,
AB2 = OA2 + OB2
OA2 = AB2 - OB2
OA2 = a2 - (a/2)2
OA2 = 3a2/4
OA = √3a/2
∵ AC = 2 × OA
AC = √3a
∴ AC : BD = √3a : a
AC : BD = √3 : 1
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In the given figure, ABCD is a rhombus in which∠C = 60°. Then, find the value of AC : BD.a)√3 : 4b)4 : √3c)√3 : 2d)√3 : 1Correct answer is option 'D'. Can you explain this answer?
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In the given figure, ABCD is a rhombus in which∠C = 60°. Then, find the value of AC : BD.a)√3 : 4b)4 : √3c)√3 : 2d)√3 : 1Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the given figure, ABCD is a rhombus in which∠C = 60°. Then, find the value of AC : BD.a)√3 : 4b)4 : √3c)√3 : 2d)√3 : 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, ABCD is a rhombus in which∠C = 60°. Then, find the value of AC : BD.a)√3 : 4b)4 : √3c)√3 : 2d)√3 : 1Correct answer is option 'D'. Can you explain this answer?.
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In the given figure, ABCD is a rhombus in which∠C = 60°. Then, find the value of AC : BD.a)√3 : 4b)4 : √3c)√3 : 2d)√3 : 1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In the given figure, ABCD is a rhombus in which∠C = 60°. Then, find the value of AC : BD.a)√3 : 4b)4 : √3c)√3 : 2d)√3 : 1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In the given figure, ABCD is a rhombus in which∠C = 60°. Then, find the value of AC : BD.a)√3 : 4b)4 : √3c)√3 : 2d)√3 : 1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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