Two side of a triangle have lengths 6 and 16 which inequalities describe the values that possible lengths for the third side

Question

asked Oct 14, 2022 189k views

1 Answer

Stumped · Answer 1 · 2022-10-19T10:53:13+0000

Answer:

22 > x > 10

10 < x < 22

Explanation:

Given

$Side\ 1 = 6$

$Side\ 2 = 16$

Required

Determine the inequality that represents the third side

Represent the third side with x.

For the triangle to be true, two of the following condition must be true.

6 + 16 > x

6 + x > 16

16 + x > 6

6 + 16 > x

22>x -- True

6 + x > 16

x > 16 - 6

x > 10 -- True

16 + x > 6

x > 6 - 16

x > -10 --- False; Because, x can't be negative.

So, we have:

22>x and
x > 10

This can be combined to give:

22 > x > 10

or

10 < x < 22