A triangle has one side that measures 1 feet and another side that measure 20 inches . Which are possible side lengths of the third side ?

Question

I need help 

Answer 1

If 20" is to be the longest of the three sides, then that third side must be > 8" but < 20".

 

If third size x" is to be greatest side, then x<32" is required.

 

Conclusion: third side x must satisfy  8 < x < 32 (all measures in inches)

 

 

Answer 2

1 foot=12 inches

you have 12, 20 and x

the sum of the lengths of any two sides of a triangle must be greater than the length of the third side

12+x>20

20+x>12

12+20>x

 

12+x>20 implies x>8

20+x>12 implies x>-8 disregard negative numbers

12+20>x implies 32>x

x>8 implies 8<x

32>x implies x<32

putting these last two inequalities together...

8<x<32

the third side must be greater than 8 inches but less than 32 inches