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In the rhombus, BC=6, AE=4, and angle DAE = 45°...

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by swerve » Tue Dec 26, 2017 2:39 pm
Image

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

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by GMATWisdom » Wed Dec 27, 2017 7:51 am
swerve wrote:Image

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

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Radius of the circle = 3
joining DE we see that AED is a right angled isosceles triangle with
Angle DAE = Angle ADE = 45.
Arc DE = Arc AGE = ½ arc AED.=(1/2)π3=3/2π (Since arc AED is a semicircle with radius 3 )
Since arc DFA is a semicircle with radius 3 therefore DFA arc= π3=3π
Distance travelled stating from C via DFAGEB and back to C
=CD+arcDFA+arcAGE+EB+BC=6+3π+(3/2)π+2+6=14+9π/2
Hence option D
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