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

Could someone please draw the figure for this? thanks

Here you go:
Hope it helps.

Key to this question is "Distinct point" and "Right Triangle". Height BD cannot be AB otherwise the points A=D. So the height BD has to come out of point B (The 90* angle) and intersect AC.

Bunuel, but D doesn't necessarily have to be inside of the triangle right? So what if point D was outside of the triangle vertically above C in your diagram, and equivalent to the original line specified BD, except outside of the triangle? If we kept the same triangle from your diagram, and instead changed the problem to say CD is a height of the triangle with D being vertically about C, then B would still be the right angle and the statements would be inefficient. Am I making a mistake in thinking this?

We are told that "points A, B, C, and D form a right triangle ABC", so D must be on one of the sides.

my question is.. we are asked ab times bc?

bt in statement 2. we have given ab*bc=24? how can we get separate value of both from this?

We are asked to find AB*BC. (2) says that AB*BC=24. So, we have the value which we wanted to find. Why do we need the values of AB and BC?

Oh doesnt ab times bc mean ab/bc? or bc/ab? ****! that means i didnt get the question clearly..!!

if ab times bc=ab*bc..fine..then i got the solution !

For statement 2:

Why can't the product BD*DC = 24 instead of being AB*BC?

Thanks
Cheers
J

BD is a height means that B is a right angle and AC is a hypotenuse (so BD is a height from right angle B to the hypotenuse AC).


(2) says that the product of the non-hypotenuse sides is equal to 24, the non-hypotenuse sides are AB and BC.

Hope it's clear.

If the perpendicular is given as 6,that means its a right triangle with base=8 and hypotenuse =10.
Is my understanding wrong?

Awesome Bunuel,Thanks a lot.

Hi Bunnel,

I have a small doubt on thic diagram. We know D is 90 degree. But I want to know how B is 90 degree. Is it because we are getting height fron one of the vertices.

Thanks.

Since, it is clear that D is the point that has the height.The height of the right triangle always comes form the 90 degree angle,thus B is 90 degree.

BD is a height means that B is a right angle and AC is a hypotenuse (so BD is a height from right angle B to the hypotenuse AC).

If the triangle is as shown in the attachment above then in statement 2 when it says the product of the non hypotenuse sides is 24
then we could also take in ∆ ABD hypotenuse is AB and non hypotenuse sides as AD *BD

also in ∆ BDC hypotenuse is BC and non hypotenuse sides are BD*DC

So statement 2 seems a bit ambiguous.

There are actually 3 right triangles in points ABCD , ∆ ABC, ∆ ABD, ∆ BDC so when they say product of non hypotenuse side
is 24 , we could choose any right triangle among these 3 and take 2 of its non hypotenuse sides .

Why are we assuming that the question is talking of ∆ ABC when it says product of non hypotenuse sides
is 24.

If question had said product of non hypotenuse sides of largest triangle or product of non hypotenuse sides of triangle ABC then 2 could surely be enough.

Please correct me if I am wrong.

Dear Bunuel,I agree with glx and I asked myself the same question above. Why we

assuming that the question is talking about ∆ ABC while the statement 2 did not say that the product of non

hypotenuse sides of largest triangle is 24 ? .