Problem named triangular region/ triangle ABC

[regina.mason56]

Hi all,

can someone explain why my thought process is wrong in the below problem?

In the diagram (don't know how to paste here, but I am hoping that instructors or someone might know which problem/diagram I am referring to) isn't AD perpendicular to BC? So from statement 1, I figured out that BD = 6 and since AD is perpendicular to BC, BD = DC.

Thanks in advance

1. If AD is 6 radical 3, and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD = 60°

(2) AC = 12

[Ben Ku]

Here is the image to the problem you're referring to.


AD cuts BC in half only if it's an isosceles triangle: if AB = AC. The question stem and statement (1) do not give us enough information to conclude that it's isosceles (we don't know that angle ABD = angle ACD). Basically we are given information about right triangle ABD, but not about right triangle ACD. Therefore (1) is insufficient.

(2) is insufficient for the same reason: we are given information about triangle ACD, but not about ABD.

Using both statements together, we can indeed conclude that AB = AC, so therefore use the information to calculate the area.

Hope that helps.