Question

Two sides of a triangle are

shown. Find the range of
values
of the third side.
9.14
k
< X <
<>

Answer 1

To find the range of values of the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So, for a triangle with sides a, b, and c, we have:

a + b > c

b + c > a

a + c > b

In this case, we know that two sides are 9 and 14. Let x be the length of the third side. Then we have:

9 + 14 > x

x + 9 > 14

x + 14 > 9

Simplifying these inequalities, we get:

23 > x

x > 5

x > -5

Therefore, the range of values of the third side is:

5 < x < 23