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03 Aug 2020, 02:27
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In the figure, ABCDEF is a regular hexagon with side 1cm. What is the area of triangle BDX?
(1) AF = FX
(2) \(\angle AFX\) = \(\angle XFE\)
Are You Up For the Challenge: 700 Level Questions
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yashikaaggarwal
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03 Aug 2020, 03:31
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BCD is a 120°,30°,30° triangle (given property of regular hexagon)
Draw a line CY from C to BD such that angle C divide into 2 equal angles of 60°
Such that BCD is divided equally into two parts of 30°,60°,90° triangle.
Of side X,√3x,2x
Where 2x = 1.
X = 1/2 = CY
Half BD = √3/2
BD = 2*√3/2 = √3
Statement 1: AF=FX = 1
No other information to drive height or sides of triangle.
(Insufficient)
Statement 2: Angle AFX = angle XFE
(No determining factor to drive value of triangle height or side)
(Insufficient)
Combining both: Extend CY to Z such that triangle BDC is similar to triangle BZD
BZ = BC
YZ = CY
And BY common.
Also BZCD is a rhombus.
BZAF and DZFE area also rhombus.
Height of triangle BDC = FX+ZF+ZY
=> 1+1+.5 = 2.5
And base = √3
Area = 1/2*2.5*√3 = 1.25√3
(Sufficient)
IMO C
Posted from my mobile device
Draw a line CY from C to BD such that angle C divide into 2 equal angles of 60°
Such that BCD is divided equally into two parts of 30°,60°,90° triangle.
Of side X,√3x,2x
Where 2x = 1.
X = 1/2 = CY
Half BD = √3/2
BD = 2*√3/2 = √3
Statement 1: AF=FX = 1
No other information to drive height or sides of triangle.
(Insufficient)
Statement 2: Angle AFX = angle XFE
(No determining factor to drive value of triangle height or side)
(Insufficient)
Combining both: Extend CY to Z such that triangle BDC is similar to triangle BZD
BZ = BC
YZ = CY
And BY common.
Also BZCD is a rhombus.
BZAF and DZFE area also rhombus.
Height of triangle BDC = FX+ZF+ZY
=> 1+1+.5 = 2.5
And base = √3
Area = 1/2*2.5*√3 = 1.25√3
(Sufficient)
IMO C
Posted from my mobile device
Attachments
IMG_20200803_155440.jpg [ 60.61 KiB | Viewed 10063 times ]
03 Aug 2020, 04:45
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Kindly see the attachment.
Concept: Need to think of properties of a regular hexagon
IMO C
Concept: Need to think of properties of a regular hexagon
IMO C
Attachments
1.jpeg [ 65.39 KiB | Viewed 9871 times ]
