Question

Two sides of a triangle measure 9 cm and 23 cm. Which could be the measure of the third side of the triangle?

Answer 1

Hello,

Let's be x the length of the 3 side (9,x,23) ==>x>0

Using inequality triangular:

9<x+23==>x>9-23==>x>-14 (done)
x<9+23==>x<32
23<x+9==>x>14

SO 14<x<32

Answer 2

Length of the third side could be any length greater than 14 cm and less than 32 cm.

Explanation:

Given:

Length of the first side = 9 cm

Length of the second side = 23 cm

To find: Possible length of the third side.

We know that the sum of two sides of a triangle is always greater than the third side.

Thus, Third side has to be less than the sum of the two given sides.

⇒ Third side < 9 + 23 = 32 cm

Also, the side can not be less the difference of the two sides.

⇒ Third side > 23 - 9 = 14 cm

Therefore, Length of the third side could be any length greater than 14 cm and less than 32 cm.