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In the figure above, the letters L, M, and N denote the area
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24 Feb 2020, 12:33
24 Feb 2020, 12:33
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Question Stats:
70% (02:16) correct
29% (00:12) wrong based on 17 sessions
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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 \(\frac{L+M}{N}\) ?
A. \(\frac{1}{2}\)
B. \(\frac{\sqrt{2}}{2}\)
C. \(1\)
D. \(\frac{\pi}{2 \sqrt{2} }\)
E. \(2 \sqrt{2}\)
Kudos for the right answer and explanation
Re: In the figure above, the letters L, M, and N denote the area
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21 Apr 2020, 17:10
21 Apr 2020, 17:10
1
Expert Reply
Since it is a right triangle, assume that the sides are 6-8-10 so that radii of the semi circles are 3-4-5
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
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
gmatclubot
Re: In the figure above, the letters L, M, and N denote the area [#permalink]
21 Apr 2020, 17:10
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