enigma123 wrote:
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.
I am struggling to understand the solution given in GMATCLub Test. Can you please explain how statement 2 is sufficient to answer this question?
Attachment:
TRIANGLE 1.jpg [ 112.83 KiB | Viewed 12079 times ]
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.