Triangle ABC is right angled at B, while triangle ACD is right angled

Hello,

Since the triangles mentioned in the problem are right-angled triangles, it is natural to think that applying the Pythagoras theorem will help us solve the problem. However, we just need to know the concept that the Hypotenuse is the longest side in a right-angled triangle, to be able to solve this problem.

Using statement 1 alone,

We can say that triangle ABC is an isosceles right-angled triangle and hence, AB = BC. However, this is grossly insufficient to find out a relationship between CD and AB, since we know neither the lengths of the sides of the triangle ACD nor the angles. Hence, statement I alone is insufficient.

Using statement II alone,

We can deduce that triangle ACD is now an isosceles right-angled triangle and hence, CD = AC. Now, in triangle ABC, AC represents the hypotenuse and is, therefore, the longest side in triangle ABC. Hence, it has to be longer than AB; so we can say that CD is definitely longer than AB. Statement II alone is sufficient.

Therefore, the answer option is B.

In such questions, a good thing to do is to draw a diagram and try to put in as many values as possible, before analysing it further. Also, a point to remember about DS questions on Geometry is that any data that gives you a UNIQUE figure/diagram is the data that is going to be sufficient and vice versa.

Hope this helps!

Cheers,
CrackVerbal Academics Team