ykaiim wrote:

Are all angles of triangle \(ABC\) smaller than 90 degrees?

1. \(2AB = 3BC = 4AC\)

2. \(AC^2 + AB^2 > BC^2\)

I am not convinced the OE. Can someone explain more on this?

You could just use substitution:

If AC = 90 then 4AC = 360

3BC = 360 then BC = 120

This wouldn't work because three angles must equal 180

If AB = 90 then 2AB = 180

3BC = 180 and BC = 60

4AC = 180 so AC = 45

90 + 60 + 45 = 195

Answer A is sufficient all are less than 90

2. If BC = 80 then AC + AB = 100

However we don't know if AC + AB = 80 + 20 or AC + AB = 95 +5

Both satisfy the equation but one has an angle greater than 90 and the other doesn't