mmslf75 wrote:Are all angles of triangle ABC smaller than 90 degrees?
1. 2AB = 3BC = 4AC
2. AC^2 + AB^2 > BC^2
OA A
pls explain !!!
Statement 1.
Consider 2AB=3BC=4AC=12K WHERE K IS CONSTANT
NOW 2AB=12K;AB=6K SIMILARLY BC=4K AND AC=3K
SO AB:BC:AC=6:4:3
THIS IMPLIES ANGLE ACB IS MORE THAN 90 DEG(THIS ANGLE WOULD HAVE BEEN 90DEG IF THE RATIO WAS 5:4:3 AND LESS THAN 90DEG IF RATIO FIRST FIGURE WOULD HAVE BEEN LESS THAN 5)
hence statement 1 is sufficient
Statement 2.
AC^2 + AB^2 > BC^2
consider AC=AB=BC, given condition satisfied.All angle less than 90deg
now consider AC=7,AB=3,BC=5 given condition satisfied ,Angle B will be more than 90Deg
So Insufficient
