# 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.**