SATHEE: Quantitative Aptitude Ques 444

Quantitative Aptitude Ques 444

Question: ABCD is a rhombus in which $ \angle C=60{}^\circ , $ Then, $ AC:BD $ is equal to

Options:

A) $ \sqrt{3}:1 $

B) 3 : 1

C) $ \sqrt{3}:\sqrt{2} $

D) 3 : 2

Show Answer

Answer:

Correct Answer: A

Solution:

ABCD is a rhombus. So, its all the sides are equal. $ BC=DC $

$ \Rightarrow $ $ \angle BDC=\angle DBC=x{}^\circ $ Also, $ \angle BCD=60{}^\circ $
In $ \Delta BCD, $ $ 2x+60{}^\circ =180{}^\circ $

$ \Rightarrow $ $ 2x=120{}^\circ $
$ \Rightarrow , $ $ x=60{}^\circ $ So, $ \Delta BCD $ is an equilateral triangle. $ BD=BC=a $ Now, $ AB^{2}=OA^{2}+OB^{2} $ $ OA^{2}=AB^{2}-OB^{2}=a^{2}-{{( \frac{a}{2} )}^{2}}=a^{2}-\frac{a^{2}}{4}=\frac{3a^{2}}{4} $ $ OA=\frac{\sqrt{3}a}{2} $

$ \therefore $ $ AC=2\times OA=\sqrt{3},a $
Thus, $ AC:BD=\frac{\sqrt{3}a}{a}=\frac{\sqrt{3}}{1} $

Quantitative Aptitude Ques 443

Quantitative Aptitude Ques 445

Quantitative Aptitude Ques 444

Question: ABCD is a rhombus in which $ \angle C=60{}^\circ , $ Then, $ AC:BD $ is equal to

Options:

Answer:

Solution:

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