How to establish condition to form a triangle when a pencil is cut into 3 parts ?
You might have solved last year CAT papers(when it was available) or any AIMCAT/SIMCAT/MOCKCAT.
You might have encountered with the various kind of problems based on properties of triangle.
Very basic properties of triangles are generally used in CAT Paper.
One such question is :
A Pencil of length 9a is cut into three parts and they form an isosceles triangle. What is the range of ‘x’ if it is the length of the equal side?
a. (3)a < x < (9/2)a
b. (9/4)a< x < (9/2)a
c. (9/4)a < x < (3)a
d. (9/4)a<= x <= (9/2)a
So how to approach this problem.
By reading the question, you will realize that the question is basically trying to check the following property of triangle.
Length of 2 sides of a triangle is greater than the third side.
Using this property lets start solving this question.
Step 1: Let the length of 3rd side be y.
So, x + x + y = 9a –> 2x + y = 9a ……….i
Step 2: x+x > y –> 2x > y
Putting value of y from (i),
x+x>9a-2x –> 4x>9a –> x>9a/4
Step 3: x+x <9a –> x<9a/2
Combining the results of x, we get the domain of x, i.e. 9a/4 < x< 9a/2. Hence option B is correct.