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# In the figure above, the area of square PQRS is 64. What is the area

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Math Expert
Joined: 02 Sep 2009
Posts: 46216
In the figure above, the area of square PQRS is 64. What is the area [#permalink]

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19 Sep 2017, 23:34
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5% (low)

Question Stats:

94% (00:34) correct 6% (01:03) wrong based on 53 sessions

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In the figure above, the area of square PQRS is 64. What is the area of ∆ QRT?

(A) 48
(B) 32
(C) 24
(D) 16
(E) 8

Attachment:

2017-09-20_1018_001.png [ 5.84 KiB | Viewed 809 times ]

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Re: In the figure above, the area of square PQRS is 64. What is the area [#permalink]

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20 Sep 2017, 00:59
Area of square PQRS = 64
Area of triangle QRT = (1/2) * b * h = (1/2) * QR * QP
Since QR * QP = side of the square * side of the square = area of the square PQRS = 64
Therefore, area of triangle QRT = (1/2) * 64 = 32
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In the figure above, the area of square PQRS is 64. What is the area [#permalink]

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20 Sep 2017, 03:23
The location of point T is not defined. So it can be any point on PS. Just think of it as a point almost overlapping with S. Then area of PTR would be very close to 32 i.e. half of 64.
Since T could be such a point, the area of every such triangle must be 32 only.

Tip: In PS questions, try to make the figure as symmetrical as you can under the given constraints, to get the answer quickly. Do just the opposite for DS questions.
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Joined: 20 Aug 2016
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Location: India
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In the figure above, the area of square PQRS is 64. What is the area [#permalink]

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20 Sep 2017, 04:16
Image

lets think it logically

area of any triangle is = (1/2)* base * height

in the figure wherever the point T belong the height of triangle will remain 8 that is the perpendicular from T to QR

so we know the length of QR that is 8 as the area of square is 64 so side is 8*8

so as now we know the base and height the area is (1/2) * 8 * 8 = 32

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Re: In the figure above, the area of square PQRS is 64. What is the area [#permalink]

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23 Sep 2017, 00:53
Bunuel wrote:

In the figure above, the area of square PQRS is 64. What is the area of ∆ QRT?

(A) 48
(B) 32
(C) 24
(D) 16
(E) 8

Attachment:
2017-09-20_1018_001.png

There is no need to even apply the formula for area of the triangle.

Since location of point T is not defined, we can assume it to be anywhere.

Consider point T to coincide with point P. This will divide the squire in 2 equal halves.

Since the area of the squire is 64, the are of triangle will be 64/2 = 32.
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Re: In the figure above, the area of square PQRS is 64. What is the area [#permalink]

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23 Sep 2017, 11:54
Side of the square= 8
T will be somewhere on the side PS but we know that it will be on the side. Thus (I inferred) that height of the triangle would equal 8.
Area= 1/2*8*8= 32
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Re: In the figure above, the area of square PQRS is 64. What is the area   [#permalink] 23 Sep 2017, 11:54
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