Question

is it possible to form a triangle with the side lengths 5.5 in, 14.5 in, and 19.9 in?
yes
no
two of a triangles side lengths are 12 inches and 5 inches. which of the following side lengths is a possible length of the third side?
17 inches
7 inches
18 inches
8 inches

Explanation:

Step1: Recall triangle - inequality theorem

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

Step2: Check if a triangle can be formed with side - lengths 5.5 in, 14.5 in, and 19.9 in

$5.5 + 14.5=20>19.9$
$5.5 + 19.9 = 25.4>14.5$
$14.5+19.9 = 34.4>5.5$
Since all three inequalities hold, a triangle can be formed.

Step3: Find the possible length of the third side for side - lengths 12 in and 5 in

Let the side - lengths of the triangle be $a = 12$, $b = 5$, and $c$ be the third side.
By the triangle - inequality theorem: $|a - b|$|12 - 5|=7$ and $12 + 5 = 17$.
So, $7

Answer:

Yes
D. 8 inches