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In the circle above, if the area of the rectangle set inside
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17 Feb 2019, 02:13
17 Feb 2019, 02:13
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In the circle above, if the area of the rectangle set inside the circle is 200 and b = 8a, what is the circumference of the circle?
A) \(25 \pi \sqrt{65}\)
B) \(5 \sqrt{65}\)
C) \(5 \pi \sqrt{13}\)
D) \(5\pi \sqrt{65}\)
E) \(5 \pi\)
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Re: In the circle above, if the area of the rectangle set inside
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18 Feb 2019, 00:30
18 Feb 2019, 00:30
1
The rectangle's diagonal is a diameter, hence angle ab is 90.
this means we can use the Pythagorus theorem: diameter^2 = a^2 + (8a)^2 = a^2+64a^2= 65a^2
diameter = root(65)a
radius = a*root(65)/2
circumference = 2pi*r=2pi*a*root(65)/2 = pi*a*root(65)
now, we also know that The rectangle's are is 200, hence a*b=200 ==> a(8a)=200 ==> 8a^2=200 ==> a^2=25 ==> a= 5
circumference = pi *5 * root65
Answer D
this means we can use the Pythagorus theorem: diameter^2 = a^2 + (8a)^2 = a^2+64a^2= 65a^2
diameter = root(65)a
radius = a*root(65)/2
circumference = 2pi*r=2pi*a*root(65)/2 = pi*a*root(65)
now, we also know that The rectangle's are is 200, hence a*b=200 ==> a(8a)=200 ==> 8a^2=200 ==> a^2=25 ==> a= 5
circumference = pi *5 * root65
Answer D
gmatclubot
Re: In the circle above, if the area of the rectangle set inside [#permalink]
18 Feb 2019, 00:30
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