MaxKirchmayer wrote:
I don't understand why 2) alone is sufficient? AB*AC=24 --> could be 3*8 or 8*3 or 4*6 or 6*4?
Please explain me, when I am wrong.
A more detailed explanation is, ABC is a right triangle, so the right angle can be either at Angle A, Angle B and Angle C.
1) But They said BD is height, and D can be any other point in the plane, can be inside or outside the triangle in any direction. That means, the 3 sides of triangle are AB, BC and AC. Since BD is height of ABC, B has to be the right angle because for right triangle, the base and height are the two non hypotenuse sides. And D doesn't is not A,B or C as it is distinct.
2) So B has to be right angle. That means either BA or BC has to be height equal to BD
3) that means, AB is either height or base and BC is the other... that makes AC as the hypotenuse
all that we need is to know is product of AB and BC
And from 3, we know that AB and BC are non hypotenuse, i.e., base and height (irrespectively) for ABC
from statements
1 AB is 6 =>
not sufficient since BC can be anything and AC can be anything,
2 product of non hypotenuse sides is 24 i.e.,
sufficient to answer
Order of preference to check is,
if one of the statements are sufficient to answer and the other isnt, the option is A or B
If both are sufficient, then option D
If none of the options are sufficient, then option is either C or E i.e., can be known by further solving
Always evaluate the options in that order.
since here, we already know statement 2 is sufficient, we don't have to solve further. so Ans B