Question

Part A is it true or false Part B which of the following could be the length of the third side

Answer 1

Answer: FALSE

Step-by-step explanation:

The rule to determine if three sides can form a triangle is that the sum of any two sides must be greater than the third side.

Let a, b, and c be the sides of the triangle:

`\begin{gathered} a=4 \\ b=12 \\ c=16 \end{gathered}`

The rule is that the following three inequalities must be met:

`\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}`

Calculating these inequalities to check if they are all true or not:

`\begin{gathered} 4+12>16\frac{}{}\rightarrow16>16 \\ 4+16>12\rightarrow20>12 \\ 12+16>4\rightarrow28>4 \end{gathered}`

The first inequality is not true, because 16 is not greater than 16 (it is equal to 16 but not greater than 16). The other two inequalities are true: 20 is greater than 12 and 28 is greater than 4.

Since one of the inequalities is not true, the lengths can not form a triangle.

Answer: FALSE