If distinct points A, B, C, and D form a right triangle ABC

Question

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 ? (1) AB=6 (2) The product of the non-hypotenuse sides is equal to 24. OPEN DISCUSSION OF THIS QUESTION IS HERE: a-b-c-and-d-are-distinct-points-on-a-plane-if-triangle-a-129328.html

piyatiwari · Answer

Answer is B.

Check out the attached diagram.

far257 · Answer

In that diagram, is AB = BD?

piyatiwari · Answer

Not necessarily. We cant say that from given info.

The question asks us to calculate AB * BC.

Statement 1, AB = 6. Not sufficient.

Statement 2, AB * BC = 24. This is what we wanted!! Sufficient.

So answer is B.

far257 · Answer

Maybe I'm confused as to what "height of a triangle" is.

piyatiwari · Answer

The height of the right triangle angle is (always) length of line which is drawn from vertex(point of 90degree) to hypotenuse and which is perpendicular to hypotenuse.

piyatiwari · Answer

Rotate the diagram clock-wise. Let the hypotenuse be its base and then find height.

Fistail · Answer

Note that points A, B, C, and D are distinct....

piyatiwari · Answer

Fistail,

Sorry, I did not get your point.

Fistail · Answer

If points A, B, C, and D are distinct, AB = BD is not possible.

Jam2014 · Answer

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.

Just thoughts in my mind and want to clear.....

Bunuel · Answer

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.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-b-c-and-d-are-distinct-points-on-a-plane-if-triangle-a-129328.html

If distinct points A, B, C, and D form a right triangle ABC

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