Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60646

In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
31 Oct 2018, 02:10
Question Stats:
69% (01:56) correct 31% (02:16) wrong based on 46 sessions
HideShow timer Statistics
In the figure above, the letters L, M, and N denote the areas of the semicircular regions whose diameters are the sides of the triangle, as shown. What is the value of (L + M)/N ? A. 1/2 B. √2/2 C. 1 D. π/(2√2) E. 2√2 Attachment:
phd02.png [ 15.19 KiB  Viewed 928 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10011
Location: Pune, India

Re: In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
31 Oct 2018, 05:39
Bunuel wrote: In the figure above, the letters L, M, and N denote the areas of the semicircular regions whose diameters are the sides of the triangle, as shown. What is the value of (L + M)/N ? A. 1/2 B. √2/2 C. 1 D. π/(2√2) E. 2√2 Since it is a right triangle, assume that the sides are 6810 so that radii of the semi circles are 345 The areas of semi circles (pi*r^2)/2 will be in the ratio of r^2 then i.e. 9:16:25 (L + M)/N = (9 + 16)/25 = 1
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)

Re: In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
31 Oct 2018, 02:13
Hi Bunuel I don't see any figure shown, can you please check?



Math Expert
Joined: 02 Sep 2009
Posts: 60646

Re: In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
31 Oct 2018, 02:17
Salsanousi wrote: Hi Bunuel I don't see any figure shown, can you please check? _______________ Fixed. Thank you.
_________________



Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)

In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
Updated on: 31 Oct 2018, 03:33
let the diameter of semicircle n be C
Using pythagorean theorem \(C^2 = A^2 + B^2\)
Area of semicircle \(= Pi * r^2 * \frac{1}{2} = Pi * \frac{D^2}{4} * \frac{1}{2} = Pi * \frac{D^2}{8}\)
From the above the area of semicircle \(N = Pi * \frac{C^2}{8}\)
Area of semicircle \(L = Pi * \frac{B^2}{8}\)
Area of semicircle \(M = Pi * \frac{A^2}{8}\)
Since B^2 + A^2 = C^2 then L+M = N
Added together \(\frac{L+M}{N}\)= \((Pi * B^2/8 + Pi *A^2/8)/Pi * C^2/8 = 1\)
Answer choice C
Originally posted by Salsanousi on 31 Oct 2018, 02:46.
Last edited by Salsanousi on 31 Oct 2018, 03:33, edited 1 time in total.



Intern
Joined: 17 Nov 2016
Posts: 12

Re: In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
31 Oct 2018, 03:21
Salsanousi wrote: let the diameter of semicircle n be C
Using pythagorean theorem \(C^2 = A^2 + B^2\)
Area of semicircle \(= Pi * r^2 * \frac{1}{2} = Pi * \frac{D^2}{4} * \frac{1}{2} = Pi * \frac{D^2}{8}\) From the above the area of semicircle N = Pi * \frac{C^2}{8}
Area of semicircle \(L = Pi * \frac{B^2}{8}\)
Area of semicircle \(M = Pi * \frac{A^2}{8}\)
Since B^2 + A^2 = C^2 then L+M = N
Added together \frac{L+M}{N}= \((Pi * B^2/8 + Pi *A^2/8)/Pi * C^2/8 = 1\)
Answer choice C Hi, Can you please explain how you got L+M =N? As per Pythagorean theorem, L^2+M^2=N^2 i understood but how did you get L+M = N Thanks Posted from my mobile device



Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)

Re: In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
31 Oct 2018, 03:35
Hi shashaankbhatYou know we get Pi * B^2/8 + Pi * A^2/8 correct? Now if we take Pi/8 as a common factor we have (B^2 + A^2) which equals C^2 So it becomes Pi/8 * C^2/ (Pi/8 * C^2) and this cancels out I hope it is clear



Intern
Joined: 17 Nov 2016
Posts: 12

Re: In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
Show Tags
31 Oct 2018, 03:44
Salsanousi wrote: Hi shashaankbhatYou know we get Pi * B^2/8 + Pi * A^2/8 correct? Now if we take Pi/8 as a common factor we have (B^2 + A^2) which equals C^2 So it becomes Pi/8 * C^2/ (Pi/8 * C^2) and this cancels out I hope it is clear Ah!! Yes. I missed it. Thank you Posted from my mobile device




Re: In the figure above, the letters L, M, and N denote the areas of the
[#permalink]
31 Oct 2018, 03:44






