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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
50% (02:59) correct
50%
(03:17)
wrong
based on 36
sessions
History
Date
Time
Result
Not Attempted Yet
Two equilateral triangles are contained in square whose side length is \(2\sqrt 3\). The bases of these triangles are the opposite side of the square, and their intersection is a rhombus. What is the area of the rhombus?
(A) 3/2
(B) \(\sqrt{3}\)
(C) \(2\sqrt{2}-1\)
(D) \(8\sqrt{3}-12\)
(E) \(\frac{4\sqrt{3}}{3}\)
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(A) 3/2
(B) \(\sqrt{3}\)
(C) \(2\sqrt{2}-1\)
(D) \(8\sqrt{3}-12\)
(E) \(\frac{4\sqrt{3}}{3}\)
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PKN
____________________________
Fixed. Kudos for noticing!
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I tried with (diagonal 1 * diagonal 2 )/2 . One of the diagonal's length will be equal to side of square, i.e, 2 \sqrt{\(3\)}. I know its wrong to assume the other diagonal will be one-third of the side of square. What is the correct approach for this question?
Tried looking at subtracting some areas from square to get rhombus but could not find a solution.
Can someone post a solution for this?
Tried looking at subtracting some areas from square to get rhombus but could not find a solution.
Can someone post a solution for this?
Refer the enclosed diagram.
GH=\(2\sqrt{3}-1-1=2\sqrt{3}-2\)
IGH & JGH are symmetrical equilateral triangles.
Area of the rhombus IGJH=2* area of equilateral triangle IGH or JGH=\(2*\frac{\sqrt{3}}{4}\)*\((2\sqrt{3}-2)^2\)=\(8\sqrt{3}-12\)
Ans. (D)
GH=\(2\sqrt{3}-1-1=2\sqrt{3}-2\)
IGH & JGH are symmetrical equilateral triangles.
Area of the rhombus IGJH=2* area of equilateral triangle IGH or JGH=\(2*\frac{\sqrt{3}}{4}\)*\((2\sqrt{3}-2)^2\)=\(8\sqrt{3}-12\)
Ans. (D)
Attachments
Rhombus.JPG [ 28.62 KiB | Viewed 3483 times ]
PKN
Hi PKN
The question says the triangles should be equilateral, triangle DIC and AJB are not equilateral, all 3 sides should be \(2\sqrt{3}\)
IMO, the figure should look something like this(Attached)
Attachments
Figure 1.png [ 15.76 KiB | Viewed 3416 times ]
neha283
Which triangles are the equilateral triangles here?
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