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17 Jan 2016, 12:08
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In the rhombus, BC = 6, AE = 4, and angle DAE = 45°. AD is the diameter of the circle. If a man started at C and followed around the outer edge of this figure to D, F, A, G, E, B, and back to C, approximately how far did he travel?
A. 14 + 27/4*π
B. 14 + 6π
C. 12 + 6π
D. 14 + 9/2*π
E. 12 + 9/2*π
Attachment:
2016-01-17_2306.png [ 7.02 KiB | Viewed 3917 times ]
17 Jan 2016, 21:33
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Bunuel
In the rhombus, BC = 6, AE , 4, and angle DAE = 45°. AD is the diameter of the circle. If a man started at C and followed around the outer edge of this figure to D, F, A, G, E, B, and back to C, approximately how far did he travel?
A. 14 + 27/4*π
B. 14 + 6π
C. 12 + 6π
D. 14 + 9/2*π
E. 12 + 9/2*π
Attachment:
2016-01-17_2306.png
Hi Bunuel,
again a good Q but there is a typo AE , 4, should be AE=4..
I'll solve it in two ways ..
first by POE and second by proper algebra..
1)POE:-
first lets look at the perimeter of rhombus one has to walk= 6+6+(6-4)=14..
our answer will be 14 + something 'π'..
A, B and D remain..
now lets look at the circle..
the radius = side of rhombus/2=6/2=3..
so perimeter of circle= 6 π...
our answer has to be less than 14+6π..
lets see A,B, and D..
A. 14 + 27/4*π= 14+6 1/4*π>14+6π.. not possible
B. 14 + 6π= 14+6π.., but our ansewr has to be less than that.. so eliminate
D. 14 + 9/2*π = 14 + 4 1/2*π <14+6π.. what we were looking for..
ans D..
2) algebric way..
GEOMETRY RULE :- if an arc(DE here) makes an angle x(45) from a point on circumference(A here), the angle from center to this arc will be 2x, 90 degree here..
Sice the arc makes a 90 angle at center, the circumference will be 2 pi *r*90/360... = 1/4 circumference..
thus he walks on 3/4 circumference..
circumference=2pi*r=6pi..
he walks 6pi*3/4=9/2pi on circle..
on rhombus he walks 6=6+2=14..
total=14+9pi/2....
D
25 Mar 2016, 22:38
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DFAG=Total Perimeter (2pi*r -2pi*r/4) ...............(1)
6+6+2=14................(2)
So 14+4.5pi
6+6+2=14................(2)
So 14+4.5pi
Attachments
Circle Rhombus.png [ 13.05 KiB | Viewed 3384 times ]
