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In the figure above, if the area of the rectangular region PQRS is 40,

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In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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New post 11 Oct 2017, 00:59
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A
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E

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  25% (medium)

Question Stats:

85% (01:12) correct 15% (01:47) wrong based on 46 sessions

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In the figure above, if the area of the rectangular region PQRS is 40, and if PT = TS, what is the area of the pentagonal region PQRST?

(A) 15
(B) 20
(C) 25
(D) 30
(E) cannot be determined

Attachment:
2017-10-11_1156_001.png
2017-10-11_1156_001.png [ 9.81 KiB | Viewed 891 times ]

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Re: In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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New post 11 Oct 2017, 01:57
IMHO: Answer E.

We don't know if T is the centre of PQRS and we don't know the relationship between sides of the triangle.
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Re: In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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New post 12 Oct 2017, 07:25
Bunuel wrote:
Image
In the figure above, if the area of the rectangular region PQRS is 40, and if PT = TS, what is the area of the pentagonal region PQRST?

(A) 15
(B) 20
(C) 25
(D) 30
(E) cannot be determined

Attachment:
2017-10-11_1156_001.png



Answer cannot be determined as we dont know the relationship between them.
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Re: In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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New post 13 Oct 2017, 09:25
Bunuel wrote:
Image
In the figure above, if the area of the rectangular region PQRS is 40, and if PT = TS, what is the area of the pentagonal region PQRST?

(A) 15
(B) 20
(C) 25
(D) 30
(E) cannot be determined

Attachment:
2017-10-11_1156_001.png


Since we don’t know the length and width of rectangle PSRS (for example, l = 10 and w = 4 OR l = 8 and w = 5), we don’t know the length of PS. Furthermore, since we do not know whether T is the center of the rectangle, there is no way for us to determine the height of triangle PTS, and thus no way to determine the area of the pentagonal region PQRST.

Alternate Explanation:

Figure not drawn to scale means that the point T could be anywhere within the rectangle that satisfies PT = TS; in other words, it could be anywhere on the vertical line that passes through T. If we imagine that point T is located very close to the side PS of the rectangle, the area of the triangle will be very small and the area of the pentagonal region will be close to the area of the rectangle. If, on the other hand, point T is located very close to the side QR of the rectangle, then the area of the triangle will be larger and the area of the pentagonal region will be smaller. Thus, the information provided in the question does not determine the area of the pentagonal region PQRST.

Answer: E
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Re: In the figure above, if the area of the rectangular region PQRS is 40, &nbs [#permalink] 13 Oct 2017, 09:25
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