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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]
11 May 2015, 08:36
If distinct points A, B, C, and D form a right triangle ABC with a height BD, what is the value of AB times BC?
1) AB = 6 2) The product of the non-hypotenuse sides is equal to 24.
So this question hinges on figuring out which angle is the right angle. According to the OA, ABC must be the right angle, but why? If all points are distinct, drawing a line from point B to point D should be impossible without making D = A or C... right? Unless I'm visualizing this wrong.
Why can't a non hypotenuse side can be BD. Why we assumed that only non-hypotenuse side are AB & BC. How do we know that Angle B is 90. why can't it be right angle at angle A and BD is just a altitude from the base BC. OR if it's given that right angle ABC, we always assume that Angle B is 90.
A, B, C, and D are distinct points on a plane. If triangle ABC is right angled and BD is a height of this triangle, what is the value of AB times BC ?
Since all points are distinct and BD is a height then B must be a right angle and AC must be a hypotenuse (so BD is a height from right angle B to the hypotenuse AC). Question thus asks about the product of non-hypotenuse sides AB and BC.
(1) AB = 6. Clearly insufficient.
(2) The product of the non-hypotenuse sides is equal to 24 → directly gives us the value of AB*BC. Sufficient.