ps test7 #18

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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

by dunkin77 » Fri Apr 06, 2007 1:21 pm

Hi,

I figured the circumstance is 3π but could not figured the triangle part. (the answer is B) )Can anyone help?

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Source: Beat The GMAT — Problem Solving | Fri Apr 06, 2007 1:21 pm

RAGS: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sun Mar 18, 2007 9:35 amFollowed by: 1 member; Location: mumbai

by RAGS » Fri Apr 06, 2007 11:43 pm

the radius is 2
circumference is 4pi
the angle inscribed at the centre of circle by the segment is 1/4 * 360=90
now draw a triangle with two sides as radius and the segment
so the triangle is a 45 45 90 triangle
the length of line segment is 2*sqrt(2)(ie hyp of the triangle)
for iso triangle below it the perpendicular to base bisects the base
so rthe lenghth of the equal side is 2+ 25=sqrt(27)=3sqrt(3)
perimeter of figure is 2*3sqrt(3) + 3pi

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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

by dunkin77 » Sat Apr 07, 2007 2:02 am

Hi,

Thank you for the explanation!

One question---how do I get "the length of line segment is 2*sqrt(2)" ?

Thank you!

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gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

by gabriel » Sat Apr 07, 2007 9:31 am

dunkin77 wrote:Hi,

Thank you for the explanation!

One question---how do I get "the length of line segment is 2*sqrt(2)" ?

Thank you!

"the length of the line segment" is the hypotenuse of the 45-45-90 triangle ... the legs of the right triqangle is 2 each so the hyp is root( 2^2+2^2) = 2sqrt(2)....

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tanyajoseph: Master | Next Rank: 500 Posts; Posts: 103; Joined: Wed May 30, 2007 6:17 amFollowed by: 1 member

by tanyajoseph » Mon Sep 17, 2007 10:22 am

"the length of the line segment" is the hypotenuse of the 45-45-90 triangle ... the legs of the right triqangle is 2 each so the hyp is root( 2^2+2^2) = 2sqrt(2)....

How do you actually derive that to 2 as the value for the legs here???
Hypotenuse you could obtain from the two legs but how do you get that part of knowing the value for the two sides to say it is 2?? Is there any shortcut or formula to obtain the length using the given height = 5??

Really appreciate any help and Thanks a ton for the help

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niks_01.27: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Wed Jun 20, 2007 12:40 pm; Location: Cleveland, OH

by niks_01.27 » Mon Sep 17, 2007 5:55 pm

This was discussed again yesterday;

https://www.beatthegmat.com/viewtopic.php?t=5230

Hope you find it useful.

regards
niks...

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