the sum of the length of any two sides of a trianhle must be greater than the length of the third side. What are possible values of x for this triangle ?

Question

Side 1: 3xcm

Side 2: x + 5

Side 3: 40cm

Answer 1

Sides:     3x       (x+5)      40

 

a)   3x + (x+5) > 40

       4x + 5 > 40

        4x < 35

        x > 8.75

 

b)     (x+5) + 40 > 3x

         x + 45 > 3x

         45 > 2x

         22.5 > x

         x < 22.5

 

c)   3x + 40 > (x+5)

         2x + 35 > 0

         2x > -35

           x > -17.5       [note: this is true for positive side lengths]

 

Combine the answers:

              8.75 cm <  x  <  22.5 cm

 

x must be between 8,75 cm and 22.5 cm.

Answer 2

3x + x + 5 > 40

4x > 35

x > 8.75 cm

 

x + 5 + 40 > 3x

45 > 2x

x < 22.5 cm