Explaination needed

[govind_raj_76]

AB,BC and CA are the sides of the Traingle ABC, Is Triangle ABC a right angle ?

1) AB:BC = 2:3

2) BC:CA = 4:5

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

[Rahul@gurome]

(1) AB: BC = 2:3 is not sufficient to find whether ABC is a right angled triangle as we don't know AC.
So, (1) is NOT SUFFICIENT to answer the question.

(2) BC: CA = 4:5 is not sufficient to find whether ABC is a right angled triangle as we don't know AB.
So, (2) is NOT SUFFICIENT to answer the question.

Combining (1) and (2), AB: BC = 2: 3 = (2)(4): (3)(4) = 8/12 and BC: CA = 4: 5 = (4)(3): (5)(3) = 12: 15.
This means AB: BC: CA = 8: 12 : 15
Now we can check whether ABC is right angled triangle by applying Pythagoras Theorem.
(15)^2 = (12)^2 + (8)^2
225 = 144 + 64
225 = 208, which is not true. So, ABC is not a right angled triangle.

The correct answer is (C).