Bunuel wrote:
Is triangle ABC a right triangle?
(1) The ratio of the largest to the smallest side of the triangle is 5 : 3.
(2) The ratio of the smallest side to the next larger side is 3 : 4.
Question stem:- Is ABC a right triangle?
St1:- The ratio of the largest to the smallest side of the triangle is 5 : 3.
Note:- Ratio relationship with the third side is not given.
Length of third side lies between 3x to 5x (both 3x and 5x are exclusive)
a)Say x=1,then measure of third side=4 , so it's a right angled triangle(3,4,5)
b)Say x=1,when measure of third side=Any value between 3 to 5 (not necessarily integers, say 3.5,4.1 etc), then it's not a right angled triangle Insufficient.
St2:- The ratio of the smallest side to the next larger side is 3 : 4
As per triangle inequality theorem, the measure of third side can be any number less than 7x(=3x+4x) and greater than x(=4x-3x).
say x=1, then the sides of the triangle would be 3,4, and 1<3rd side<7.
Insufficient.
Combined,
Sides of the triangle are in the ration 3k:4k:5k.
So, the triangle ABC is a right angled triangle.
Ans. (C)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine