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The figure above consists of an isosceles triangle and 7 semicircles,

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The figure above consists of an isosceles triangle and 7 semicircles,  [#permalink]

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New post 28 Nov 2017, 21:21
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  25% (medium)

Question Stats:

84% (01:02) correct 16% (01:07) wrong based on 27 sessions

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The figure above consists of an isosceles triangle and 7 semicircles, each having the same diameter. If the perimeter of the triangle is 28, what is the radius of one of the semicircles?

(A) 1
(B) 2
(C) 4
(D) 6
(E) 7

Spoiler: ::
Attachment:
2017-11-29_0807_001.png
2017-11-29_0807_001.png [ 27.25 KiB | Viewed 573 times ]
Spoiler: OA

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Re: The figure above consists of an isosceles triangle and 7 semicircles,  [#permalink]

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New post 28 Nov 2017, 21:23
B

Let d be the diameter of the semicircle.
We have 7d=28.
Hence d=4

Radius =2


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Re: The figure above consists of an isosceles triangle and 7 semicircles,  [#permalink]

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New post 28 Nov 2017, 22:22
let us take the 2 equal sides to be = x .
let us take the unequal side = y=diameter of the circle(from the figure)
given : perimeter=28.
i.e 2x+y=28.......(i)
from the figure and given information,
3y=x...........(ii)

substituting equation (ii) in equation (i).


7y=28. this is implies that y=4
radius=2.
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Re: The figure above consists of an isosceles triangle and 7 semicircles,  [#permalink]

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New post 01 Dec 2017, 07:54
Bunuel wrote:
Image
The figure above consists of an isosceles triangle and 7 semicircles, each having the same diameter. If the perimeter of the triangle is 28, what is the radius of one of the semicircles?

(A) 1
(B) 2
(C) 4
(D) 6
(E) 7

Spoiler: ::
Attachment:
2017-11-29_0807_001.png


We see that the perimeter of the triangle is equivalent to 7 diameters; thus, each diameter must be equal to 4, so the radius of any one of the circles is 2.

Answer: B
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Re: The figure above consists of an isosceles triangle and 7 semicircles, &nbs [#permalink] 01 Dec 2017, 07:54
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