Question

A triangle has sides measuring 8 inches and 12 inches.If x represent the length in inches of the third side, which inequality gives the range of possible values for x

Answer 1

Hello,

Each side of a triangle is less than the sum of the 2 others sides;

x<8+12 ==>x<20
8<x+12 already realized
12<x+8==>x>4
So:

4<x<20 (i suppose that all the vertex are not on the same line)

Answer 2

The range of possible values for x is:

4<x<20

Explanation:

For a,b and c to be the sides of a triangle following inequalities must be satisfied

a<b+c , b<a+c and c<a+b

Here a=8

b=12

and c=x

8<12+x , 12<8+x and x<12+8

i.e. 8-12<x , 12-8<x and x<20

i.e. -4<x , 4<x and x<20

i.e. 4<x<20

Hence, the range of possible values for x is:

4<x<20