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# In the figure above, arc SBT is one quarter of a circle with center R

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Math Expert
Joined: 02 Sep 2009
Posts: 47015
In the figure above, arc SBT is one quarter of a circle with center R [#permalink]

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23 Nov 2017, 01:22
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Question Stats:

45% (02:04) correct 55% (02:25) wrong based on 22 sessions

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In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of the shaded region is

(A) 8 + 3π
(B) 10 + 3π
(C) 14 + 3π
(D) 1 + 6π
(E) 12 + 6π

Attachment:

2017-11-23_1215_001.png [ 13.95 KiB | Viewed 1832 times ]

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Joined: 14 Oct 2015
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Re: In the figure above, arc SBT is one quarter of a circle with center R [#permalink]

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23 Nov 2017, 17:41
1
Bunuel wrote:

In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of the shaded region is

(A) 8 + 3π
(B) 10 + 3π
(C) 14 + 3π
(D) 1 + 6π
(E) 12 + 6π

Attachment:
2017-11-23_1215_001.png

It should be B.

Length of Arc is quarter of circumference of circle so

$$Arc = 2πr/4 = 2π6/4 = 3π$$

Rectangle ABCR is sum of two triangles $$\triangle ABC$$ and $$\triangle ARC$$ where diagonals $$RB$$ and $$AC$$ are equal to radius of the Circle. If it were a regular quarter circle, perimeter would have been 3π + 2*radius. However, It appears the shaded region just subtracts length and breadth of the rectangle (given as 8) from the two radius and bypasses it with the diagonal of the rectangle instead.

$$3π + 12 - 8 + 6 = 10 + 3π$$
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Re: In the figure above, arc SBT is one quarter of a circle with center R [#permalink]

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23 Nov 2017, 23:41
2
Bunuel wrote:

In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of the shaded region is

(A) 8 + 3π
(B) 10 + 3π
(C) 14 + 3π
(D) 1 + 6π
(E) 12 + 6π

Attachment:
2017-11-23_1215_001.png

Perimeter of shaded region = Perimeter of quarter circle SRT - (Length + Width of rectangle) + Diagonal of rectangle (AC)

The diagonal of the rectangle is same as the radius of the circle i.e. 6.

Perimeter of quarter circle SRT = 6 + 6 + (1/4)*2π*6 = 12 + 3π

Perimeter of shaded region = 12 + 3π - 8 + 6 = 10 + 3π

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Re: In the figure above, arc SBT is one quarter of a circle with center R   [#permalink] 23 Nov 2017, 23:41
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# In the figure above, arc SBT is one quarter of a circle with center R

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