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In the triangle above, which of following is correct about the length
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02 Feb 2024, 05:06
02 Feb 2024, 05:06
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66% (03:13) correct
33% (03:12) wrong based on 6 sessions
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GRE In the triangle above, which of following is correct about the length of AE.jpg [ 18.83 KiB | Viewed 730 times ]
In the triangle above, which of following is correct about the length of AE?
Indicate all correct options.
(A) \(3 \sqrt{2}<AE< 4 \sqrt{3}\)
(B) \(AE > CE\)
(C) \(AE = DE\)
(D) \(AE^2 + CD^2= 12^2\)
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: In the triangle above, which of following is correct about the length
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02 Feb 2024, 09:48
02 Feb 2024, 09:48
1
The answers are A and D.
∠ACB = 180 - 20 - 80 = 80° --> ABC is an isosceles triangle and AB = AC = 15
Since ∠BCD = 110° --> ∠ECD = 110 - 80 = 30°
& CDE is a 30:60:90 right triangle.
--> Ration of sides in the order 30:60:90 = x : x√3 : 2x
--> DC = 2x = 6√3
--> ED = x = 6√3/2
--> EC = x√3 = (6√3/2) * √3 = 9
--> AE = AC - EC = 15 - 9 = 6
Therefore:
3√2 < AE < 4√3 --> CORRECT
AE > CE --> INCORRECT
AE = DE --> INCORRECT
AE^2 + CD^2 = 12^2 --> 6^2 + (6√3)^2 = 36 + 108 = 144 --> CORRECT
∠ACB = 180 - 20 - 80 = 80° --> ABC is an isosceles triangle and AB = AC = 15
Since ∠BCD = 110° --> ∠ECD = 110 - 80 = 30°
& CDE is a 30:60:90 right triangle.
--> Ration of sides in the order 30:60:90 = x : x√3 : 2x
--> DC = 2x = 6√3
--> ED = x = 6√3/2
--> EC = x√3 = (6√3/2) * √3 = 9
--> AE = AC - EC = 15 - 9 = 6
Therefore:
3√2 < AE < 4√3 --> CORRECT
AE > CE --> INCORRECT
AE = DE --> INCORRECT
AE^2 + CD^2 = 12^2 --> 6^2 + (6√3)^2 = 36 + 108 = 144 --> CORRECT
gmatclubot
Re: In the triangle above, which of following is correct about the length [#permalink]
02 Feb 2024, 09:48
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