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# In the figure above, arcs PR and QS are semicircles with centers at Q

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Math Expert
Joined: 02 Sep 2009
Posts: 42579

Kudos [?]: 135467 [1], given: 12695

In the figure above, arcs PR and QS are semicircles with centers at Q [#permalink]

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28 Nov 2017, 20:19
1
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Expert's post
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(N/A)

Question Stats:

91% (00:50) correct 9% (01:41) wrong based on 22 sessions

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In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

[Reveal] Spoiler:
Attachment:

2017-11-29_0807.png [ 32.32 KiB | Viewed 415 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135467 [1], given: 12695

Intern
Joined: 07 Feb 2017
Posts: 13

Kudos [?]: 0 [0], given: 5

Location: India
Concentration: Operations, Operations
GMAT 1: 610 Q48 V26
GPA: 3.7
WE: Engineering (Manufacturing)
Re: In the figure above, arcs PR and QS are semicircles with centers at Q [#permalink]

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28 Nov 2017, 21:42
The radius of both the circles is equal and is 5 . Hence, the total perimeter is equal to 2πR+2R.
Hence the perimeter is equal to 10πr+10.

Kudos [?]: 0 [0], given: 5

VP
Joined: 22 May 2016
Posts: 1119

Kudos [?]: 400 [1], given: 640

In the figure above, arcs PR and QS are semicircles with centers at Q [#permalink]

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30 Nov 2017, 15:21
1
KUDOS
Bunuel wrote:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

[Reveal] Spoiler:
Attachment:
2017-11-29_0807.png

Because semicircle PR is centered at Q, its radius = QR = PQ (given) = 5. Because semicircle QS is centered at R, its radius, too, is QR = 5.

Perimeter:

Segment PQ = 5
Segment RS = 5

Arc PR = $$\frac{2πr}{2}=\frac{10π}{2}= 5π$$

Arc QS = $$\frac{2πr}{2}=\frac{10π}{2}= 5π$$

Total: 10 + 10π

Kudos [?]: 400 [1], given: 640

Manager
Joined: 04 Dec 2016
Posts: 56

Kudos [?]: 12 [0], given: 42

Re: In the figure above, arcs PR and QS are semicircles with centers at Q [#permalink]

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30 Nov 2017, 19:17
Bunuel wrote:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

[Reveal] Spoiler:
Attachment:
2017-11-29_0807.png

we have r = 5 for each circle
perimeter of half circle = Pi * r

so perimeter of the shaded region = perimeter of both half circles + r1 + r2 = 2*5*pi + 5 + 5 = 10pi + 10

Kudos [?]: 12 [0], given: 42

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1931

Kudos [?]: 1015 [0], given: 3

Location: United States (CA)
Re: In the figure above, arcs PR and QS are semicircles with centers at Q [#permalink]

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01 Dec 2017, 06:53
Bunuel wrote:

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what is the perimeter of the shaded region?

(A) 5π + 5
(B) 5π + 15
(C) 10π + 10
(D) 10π + 15
(E) 100π

[Reveal] Spoiler:
Attachment:
2017-11-29_0807.png

We see that the radii of both semicircles is 5.

Thus, the semicircular arc of each semicircle (half circumference) is 1/2 x 2π(5) = 5π. We also see that PQ = RS = 5. Thus the perimeter of the shaded region is:

5π + 5π + 5 + 5 = 10π + 10

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Kudos [?]: 1015 [0], given: 3

Re: In the figure above, arcs PR and QS are semicircles with centers at Q   [#permalink] 01 Dec 2017, 06:53
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