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Triangle ABC has vertices A(3,0) , B(6,0) and C(a,b)

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Triangle ABC has vertices A(3,0) , B(6,0) and C(a,b)  [#permalink]

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New post 02 Aug 2018, 02:59
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Triangle ABC has vertices A(3,0) , B(6,0) and C(a,b) in the xy-Plane. What is the area of the triangle ?

(1) a = 4
(2) b = 5
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Triangle ABC has vertices A(3,0) , B(6,0) and C(a,b)  [#permalink]

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New post 02 Aug 2018, 03:49
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1
Point A and B gives the length of base AB. To find area, we need height.
Since y coordinate of A and B is same, hence it is parallel to X axis.
It means we only need y coordinate of C to find the altitude/height of the triangle ABC. We need b of C(a,b)
1) a = 4. NOT SUFFICIENT.
2) b = 5. Bingo, this is what we were looking for.
SUFFICIENT.

Answer B.
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Re: Triangle ABC has vertices A(3,0) , B(6,0) and C(a,b)  [#permalink]

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New post 02 Aug 2018, 04:24
Amankatyal wrote:
Triangle ABC has vertices A(3,0) , B(6,0) and C(a,b) in the xy-Plane. What is the area of the triangle ?

(1) a = 4
(2) b = 5

Area of triangle ABC=\(\frac{1}{2}*(6-3)*height\)
So,we require height of the triangle(vertical distance from horizontal axis) or length of other two sides of the triangle.
St1:- a=4 or x co-ordinate of unknown vertex is 4. No information on y-coordinate or b.
So insufficient.
St2:- b=5 or vertical position of the vertex C is 5.
So co-ordinate of C could be (+/-/0,5). We are not interested in the horizontal position of C since we have got the vertical position or height .So, area can be calculated.And it is evident from the area formula that area is not dependent on the horizontal position of C. So, irrespective of the value of 'a' , area of triangle ABC is same.
Sufficient.
Ans (B)
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Re: Triangle ABC has vertices A(3,0) , B(6,0) and C(a,b) &nbs [#permalink] 02 Aug 2018, 04:24
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