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What is the area of right triangle ABC?

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What is the area of right triangle ABC?  [#permalink]

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New post 23 Jan 2015, 07:39
1
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:00) correct 28% (00:53) wrong based on 174 sessions

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Re: What is the area of right triangle ABC?  [#permalink]

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New post 23 Jan 2015, 10:06
ans C...
1) insufficient.. triangle could be with sides 5,12,13 or 5,13,\sqrt{}194
2) insufficient.
combined sufficient
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Re: What is the area of right triangle ABC?  [#permalink]

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New post 23 Jan 2015, 10:29
1
In a triangle, if we have a set of s-a-s (side - angle - side), we can know the area of that triangle. (Even can solve any measurement of that triangle).

S1. 2 side (only)
S2. 1 angle (only)

Combine 2 side and 1 angle between the two sides => Sufficient. Answer C.

Note: in this case we don't have to use the information of "right triangular".
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Re: What is the area of right triangle ABC?  [#permalink]

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New post 23 Jan 2015, 13:53
1
Stmt 1: Just 2 sides given. third side would be varied depending on the angle its forming between the two sides. so insufficient
stmt 2: just angle given. we do not know sides of the triangle.so insufficient

Combining 1& 2
angle ABC =90, AB=5, BC=13, we can calculate area

So answer is C
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Re: What is the area of right triangle ABC?  [#permalink]

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New post 26 Jan 2015, 04:40
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Bunuel wrote:
What is the area of right triangle ABC?

(1) Side AB measures 5 meters and Side BC measures 13 meters

(2) Angle ABC measures 90 degrees.

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

One terrific property of right triangles is that two sides form a right angle, meaning that those two sides can be used as the base and height to find the area (or, if you're given the area, you can use that area and one of the sides to find the other). The key, though, is recognizing that you need to have two perpendicular sides in order to call them base and height - the hypotenuse, the long side, is not perpendicular to either of the other two sides.

In this case, statement 1 may suggest a 5-12-13 triangle, so you may be tempted to immediately use the 5 and 12 sides to find the area. But since you don't know whether the side of 13 is another short side or whether it is the hypotenuse, you can't quite make that determination just yet.

Statement 2 is not sufficient on its own - with only 2 you don't know any lengths at all - but when paired with the lengths from statement 1 you now know that B is the right angle so sides AB and BC are the two short sides, and can therefore use those lengths to find that the area is 32.5 square meters. The correct answer is C.
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Re: What is the area of right triangle ABC?  [#permalink]

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New post 27 Aug 2017, 05:50
S1: Given 2 sides, but unable to determine the hypotenuse

S2: Given the right angle, but no sides

Whn combined sufficient t detrmine the legs and hypotenuse , hence ans:C
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Re: What is the area of right triangle ABC?   [#permalink] 27 Aug 2017, 05:50
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