MATH SOLVE

9 months ago

Q:
# By the Triangle Inequality Theorem, if two sides of a triangle have lengths of 6 and 13, what are the possible lengths of the third side?

Accepted Solution

A:

The Triangle Inequality Theorem establishes that the length of the triangle is shorter than the sum of the two lenghts of the others two sides. Then, you have:

a=6 (the lenght of a side of the triangle).

b=13 (the lenght of a side of the triangle).

c=x (the length of the third side).

Therefore:

c<a+b

c<6+13

c<19

The lenght of the third side is:

(13-6)<c<19

7<c<9

a=6 (the lenght of a side of the triangle).

b=13 (the lenght of a side of the triangle).

c=x (the length of the third side).

Therefore:

c<a+b

c<6+13

c<19

The lenght of the third side is:

(13-6)<c<19

7<c<9