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BELOW IS REVISED VERSION OF THIS QUESTION WITH A SOLUTION:

A, B, C, and D are distinct points on a plane. If triangle ABC is a 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.

Guys , I think I cldnt explain my problem. Im not talking of OA. OA is B indeed 2 which i agree. My question is why is point D given in the question. there is no need for this. In case its a triangle, there have 2b only 3 points na? also BD height is confusing me.

D is given to make question tough and intresting. Also it gave a twist in the question. The way this question is designed, D is required and correctly signals the right angle as well.
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Guys , I think I cldnt explain my problem. Im not talking of OA. OA is B indeed 2 which i agree. My question is why is point D given in the question. there is no need for this. In case its a triangle, there have 2b only 3 points na? also BD height is confusing me.

D is given to make question tough and intresting. Also it gave a twist in the question. The way this question is designed, D is required and correctly signals the right angle as well.

BD is the Height to the Hypotenuse. In the right trinagle the non hypotenuse sides are the other heigts of the triangle. It is given in order to identify the Hypotenuse.

Since the triangle has ABC as a right triangle, the square of the triangle would be multiple of two non hypothenuse sides of the triangle divided by two. Statement ! just provides us with the information about the measurement of side AB Not sufficient.

Hence, we know that 2) The product of the non-hypotenuse sides is equal to 24, which is multiple of sides AB and BC (reuqired sides) We can conclude that Statement 2 is sufficient to answer the question.

Please, give me kudos, if you like my answer...
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Since all points are distinct and BD is the height...D lies on AC and AC is hypotenueus. The right angle is formed at B. In all other scenarios, D equals either A/C

I assumed that D should be a distinct pt. However, if the triangle is right-angled at A then the altitude BD can be drawn outside the triangular region ABC such that the BD will be parallel to AB or AC. In this case, the value of AB*BC will be 6*sqrt(52), which is different from the ans that we get if we assume that the triangle is right angled at B.

I have a small question, If ABC froms a right angled triangle then the height should be either AB or BC or AC, then how did D come into the picture. I think this can be possible only when the point D coincides with any one of A, B or C.

Could you explain if i got this wrong.

Thanks

x2suresh wrote:

dzyubam wrote:

Tvisha wrote:

Distinct points A , B , C , 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

could any one explain this?

I've added the missing text.

Thanks dzyubam for correcting the question.

Answer should be B. AB*BC = itself is product of non-hypotenuse sides.