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09 Oct 2019, 02:20
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D
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Difficulty:
95%
(hard)
Question Stats:
16% (02:31) correct
84%
(02:32)
wrong
based on 37
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In the figure below, BD = 2DC and AD = BD, what is the value of AB?
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09 Oct 2019, 04:25
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KSBGC
Let CD=x, so BD=2x....BCD is a right angled triangle with hypotenuse and one side in ratio 2:1, so it is a \(1:\sqrt{3}:2\) right angled triangle. BC=\(\sqrt{3}\)x
Now, AD=BD, so AC=CD+AD=x+2x=3x
Take triangle ABC, which is also a right angled triangle with sides \(\sqrt{3}\) and 3x, so the hypotenuse AB= \(\sqrt{(3x)^2+(\sqrt{3}x)^2}=\sqrt{9x^2+3x^2}=\sqrt{12x^2}=2x\sqrt{3}=BD\sqrt{3}\), as \(2x=BD=CD\)
B
Also, \(BD\sqrt{3}=2CD\sqrt{3}=2BC\), as \(CD\sqrt{3}=BC\)
D
So, you have two answers in given choices..
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30 Jul 2025, 06:27
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