Question

The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 23cm and a second side that is 4cm less than twice the third side, what are the possible lengths for the second and third sides?

Answer 1

21 < x < 27

Explanation:

Given that :

Side 1 = 23

Side 3 = x

Side 2 = 2x - 4

23 + x > 2x - 4

Collect like terms

x - 2x > - 4-23

-x > - 27

x < 27

Also ;

23 + 2x - 4 > x

23 - 4 > x - 2x

21 > - x

-21 < x

x > - 21

Hence,

Possible values of x :

x > 21 and x < 27

21 < x < 27