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29 Jun 2021, 01:30
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C
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Difficulty:
25%
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Question Stats:
79% (02:14) correct
21%
(02:19)
wrong
based on 61
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In the figure above, ABC is an isosceles right triangle. Line segment AC defines semicircle S1 and legs AB and BC define semicircles S2 and S3 respectively. Two ants walk from A to C, The red ant walks along S1 and the black ant walks along S2 and then along S3. What is the ratio, by distance, of the path of the black ant to the path of the red ant?
A. 1:2
B. 2:1
C. √2:1
D. 1:√2
E. √2:π
Attachment:
1.png [ 11.71 KiB | Viewed 2933 times ]
29 Jun 2021, 02:37
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Dia of s2 and s3 = x
Dia of s1 = \(\sqrt{2x}\)
A = Circumference of s2 = pi* x/2
B = Circumference of s3 = pi* x/2
C = Circumference of s1 =\( pi* \frac{\sqrt{2}x}{2}\\
\)
Ratio of paths = A+ B / C =√2:1
Dia of s1 = \(\sqrt{2x}\)
A = Circumference of s2 = pi* x/2
B = Circumference of s3 = pi* x/2
C = Circumference of s1 =\( pi* \frac{\sqrt{2}x}{2}\\
\)
Ratio of paths = A+ B / C =√2:1
Bunuel
asishron29181
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Given Kudos: 68
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
29 Jun 2021, 03:46
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Given ABC is isosceles right triangle.
Let AB = BC = 4 cm
AC =4√ 2 cm
Let the path of black ant = P1
path of red ant = P2
Semi perimeter =pie *r
Path covered by P1 = π* r + π * r
=2*π*r = 4*π
Path covered by P2 = π*r
=π*2√ 2
Ratio of P1 : P2 = 4*π/ π*2√ 2
=√ 2: 1
IMO C
Let AB = BC = 4 cm
AC =4√ 2 cm
Let the path of black ant = P1
path of red ant = P2
Semi perimeter =pie *r
Path covered by P1 = π* r + π * r
=2*π*r = 4*π
Path covered by P2 = π*r
=π*2√ 2
Ratio of P1 : P2 = 4*π/ π*2√ 2
=√ 2: 1
IMO C
