Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60560

If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
09 Sep 2018, 08:09
Question Stats:
60% (03:10) correct 40% (03:01) wrong based on 91 sessions
HideShow timer Statistics
If side BX has length 10 and side AC has length 8, what is the area of the shaded region? A. \(2\sqrt{3}\) B. \(4\sqrt{3}\) C. \(6\sqrt{3}\) D. \(8\sqrt{3}\) E. \(12\sqrt{3}\) Attachment:
image019.jpg [ 4.04 KiB  Viewed 1495 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 987
WE: Supply Chain Management (Energy and Utilities)

If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
09 Sep 2018, 09:06
Bunuel wrote: If side BX has length 10 and side AC has length 8, what is the area of the shaded region? A. \(2\sqrt{3}\) B. \(4\sqrt{3}\) C. \(6\sqrt{3}\) D. \(8\sqrt{3}\) E. \(12\sqrt{3}\) Area of the shaded region=Area of right angled triangle BOC (309060) (Refer enclosed figure) ABC is a 309060 triangle, Hence \(BC=\frac{AC}{2}=\frac{8}{2}=4\) Now in the triangle BOC(309060) , Base=OC=\(\frac{4}{2}\)=2, height=OB=\(2\sqrt{3}\) So, area of triangle BOC(shaded region)=\(\frac{1}{2} *OC*OB=\frac{1}{2} *2*2\sqrt{3}\)=\(2\sqrt{3}\) Ans. (A)
Attachments
circle.png [ 37.92 KiB  Viewed 1382 times ]
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Intern
Joined: 19 Sep 2016
Posts: 46

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
15 Sep 2018, 07:49
Please explain the solution. Thanks. !!



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 987
WE: Supply Chain Management (Energy and Utilities)

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
15 Sep 2018, 08:51
siddharthfrancis wrote: Please explain the solution. Thanks. !! Hi siddharthfrancis, Detailed explanation has been provided in the above post. You may raise specific queries(if any).
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Director
Joined: 04 Sep 2015
Posts: 675
Location: India
WE: Information Technology (Computer Software)

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
15 Sep 2018, 12:09
PKN wrote: siddharthfrancis wrote: Please explain the solution. Thanks. !! Hi siddharthfrancis, Detailed explanation has been provided in the above post. You may raise specific queries(if any). trianlge 306090 is fine, how did we get BC=AC/2? what rule?



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 987
WE: Supply Chain Management (Energy and Utilities)

If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
15 Sep 2018, 13:12
abhishekdadarwal2009 wrote: PKN wrote: siddharthfrancis wrote: Please explain the solution. Thanks. !! Hi siddharthfrancis, Detailed explanation has been provided in the above post. You may raise specific queries(if any). trianlge 306090 is fine, how did we get BC=AC/2? what rule? Hi siddharthfrancis abhishekdadarwal2009, In the triangle ABC , Angle A=30, Angle C=60, Angle B=90 So the corresponding sides are in the ratio: BC:AB:AC=x:√3x:2x Or, BC=x and AC=2x Or, AC is 2 times BC Or, BC=AC/2 You may go thru the below link for a detailed insight on SPECIAL TRIANGLES. https://gmatclub.com/forum/mathtriangles87197.htmlHope your query is nullified. Thank you.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Director
Joined: 04 Sep 2015
Posts: 675
Location: India
WE: Information Technology (Computer Software)

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
15 Sep 2018, 13:29
Hi siddharthfrancis abhishekdadarwal2009, In the triangle ABC , Angle A=30, Angle C=60, Angle B=90 So the corresponding sides are in the ratio: BC:AB:AC=x:√3x:2x Or, BC=x and AC=2x Or, AC is 2 times BC Or, BC=AC/2 You may go thru the below link for a detailed insight on SPECIAL TRIANGLES. https://gmatclub.com/forum/mathtriangles87197.htmlHope your query is nullified. Thank you.[/quote] Now i understand that we use the 306090 rule on the bigger triangle to find one comman side, and then wth that side we use 306090 on the smaller trianlge to find the lenghts of the sides of the triangle and thus finding the area of the smaller triangle. thanks.



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 987
WE: Supply Chain Management (Energy and Utilities)

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
15 Sep 2018, 13:32
abhishekdadarwal2009 wrote: Hi siddharthfrancis abhishekdadarwal2009, In the triangle ABC , Angle A=30, Angle C=60, Angle B=90 So the corresponding sides are in the ratio: BC:AB:AC=x:√3x:2x Or, BC=x and AC=2x Or, AC is 2 times BC Or, BC=AC/2 You may go thru the below link for a detailed insight on SPECIAL TRIANGLES. https://gmatclub.com/forum/mathtriangles87197.htmlHope your query is nullified. Thank you. Now i understand that we use the 306090 rule on the bigger triangle to find one comman side, and then wth that side we use 306090 on the smaller trianlge to find the lenghts of the sides of the triangle and thus finding the area of the smaller triangle. thanks.[/quote] Your reasoning bears zero fallacies. You are welcome.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Senior Manager
Joined: 27 Dec 2016
Posts: 304

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
15 Sep 2018, 19:08
Hi BunuelCould you please explain where I made a mistake in my solution? I got B as my answer. My strategy was to find the area of ABC and BXY. Then subtracting these two to find the area of BOC. Area of ABC= 1/2*(4√3)*4 = 8√3 Area of BXY = 1/2*(5√3)*5= 12.5√3 Area of the shaded region: 12.5√3  8√3= 4.5√3 Please help! Thank You!



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 987
WE: Supply Chain Management (Energy and Utilities)

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
17 Sep 2018, 23:08
csaluja wrote: Hi BunuelCould you please explain where I made a mistake in my solution? I got B as my answer. My strategy was to find the area of ABC and BXY. Then subtracting these two to find the area of BOC.
Area of ABC= 1/2*(4√3)*4 = 8√3 Area of BXY = 1/2*(5√3)*5= 12.5√3 Area of the shaded region: 12.5√3  8√3= 4.5√3 Please help! Thank You! Hi csaluja , I have highlighted the mistake in reasoning in red color.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Senior Manager
Joined: 27 Dec 2016
Posts: 304

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
18 Sep 2018, 07:29
PKN wrote: csaluja wrote: Hi BunuelCould you please explain where I made a mistake in my solution? I got B as my answer. My strategy was to find the area of ABC and BXY. Then subtracting these two to find the area of BOC.
Area of ABC= 1/2*(4√3)*4 = 8√3 Area of BXY = 1/2*(5√3)*5= 12.5√3 Area of the shaded region: 12.5√3  8√3= 4.5√3 Please help! Thank You! Hi csaluja , I have highlighted the mistake in reasoning in red color. Hi PKN, Could you please explain why the highlighted part is incorrect? Would greatly appreciate it!



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 987
WE: Supply Chain Management (Energy and Utilities)

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
18 Sep 2018, 18:36
csaluja wrote: PKN wrote: csaluja wrote: Hi BunuelCould you please explain where I made a mistake in my solution? I got B as my answer. My strategy was to find the area of ABC and BXY. Then subtracting these two to find the area of BOC.
Area of ABC= 1/2*(4√3)*4 = 8√3 Area of BXY = 1/2*(5√3)*5= 12.5√3 Area of the shaded region: 12.5√3  8√3= 4.5√3 Please help! Thank You! Hi csaluja , I have highlighted the mistake in reasoning in red color. Hi PKN, Could you please explain why the highlighted part is incorrect? Would greatly appreciate it! Hi csaluja, According to your reasoning , Area of BOC= Area of ABCArea of BXY Let's break the area of ABC and BXY in terms of area of BOC, Area of ABC= Area of AOB+Area of BOC(1) Area of BXY=Area of XOCY+Area of BOC(2) Now, subtracting (2) from(1) ,we have Area of ABCArea of BXY=Area of AOBArea of XOCY, which is not equal to area of BOC. Hope it's clear.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



NonHuman User
Joined: 09 Sep 2013
Posts: 13993

Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
Show Tags
30 Nov 2019, 09:54
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: If side BX has length 10 and side AC has length 8, what is the area of
[#permalink]
30 Nov 2019, 09:54






