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The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle
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28 Jul 2017, 09:01
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The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90°, what is the area of triangle ABC? A. 102 B. 120 C. 132 D. 144 E. 256
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Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle
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28 Jul 2017, 09:14
Given that triangle ABC is right angled at B, we know that the x coordinate of B and the x coordinate of C should be equal. Equating both, we get a equals 5.5. Substitute into the points and the base comes out to be 17 units while the height is 12. Area is 17*12/2 which is 102. Sent from my ONE A2003 using GMAT Club Forum mobile app



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Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle
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29 Jul 2017, 01:54
We know that since Y coordinate of point B and y coordinate of point C is equal (Triangle ABC is 90 at B)
Therefore equating the the y coordinates of both the points B and C
i.e 4a  5 = 2a + 6
We get, a = 11/2
Substituting the value of a in the coordinate points. Hence the points are now A (0,0), B (0,17) and C(12,17)
Area of triangle ABC = 1/2 x 12 x 17 = 102
Answer (A) = 102



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Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle
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29 Jul 2017, 02:53
Bunuel wrote: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90°, what is the area of triangle ABC?
A. 102 B. 120 C. 132 D. 144 E. 256 ABC is a right angle triangle, right angled at B. ABC = 90° Now A(0,0) and B (0, 4a5) represents Yaxis.. So, BC must be perpendicular to Y  axis i.e. BC must be parallel to Xaxis So. 4a5=2a+6 > 2a = 11 > a = 5.5 So, 4a 5 = 17 2a+1 = 12 2a+6 = 17 So, the points are A(0,0) , B(0,17) and C(12,17) AB = 17 BC = 12 Area (tria ABC) = 1/2*17*12 = 17 * 6 = 102 Answer A
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Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle
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29 Jul 2017, 10:02
Bunuel wrote: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90°, what is the area of triangle ABC?
A. 102 B. 120 C. 132 D. 144 E. 256 • A very interesting testing our skill of visualization. • A is the origin and B lies on the yaxis.
o If ABC is a rightangled triangle, that mean angle B = 90 degrees. o Also, line BC is a parallel to the xaxis.
Thus, the ycooridante of B and C would be the same. • \(4a – 5 = 2a + 6\) • \(2a = 11\) • \(a = 5.5\) • The area of the triangle \(= \frac{1}{2} * AB * BC = \frac{1}{2} * (4a 5) * (2a+1)\)
o We know that \(a = 5.5\), substituting the value in the equation above, we get –
\(Area = \frac{1}{2} * (225)*12\) \(Area = 102\) • And the correct answer is Option A.
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Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle
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29 Jul 2017, 10:02






