Question

Decide whether each set of numbers can form a triangle. Be sure to show work. 1-) 8,10 and 9

Answer 1

Let's begin by listing out the information given to us:

Side 1 (a) = 8

Side 2 (b) = 10

Side 3 (c) = 9

To determine if these set of numbers can form a triangle, we will use the Triangle Inequality Theorem which states that the sum of two side lengths of a triangle is greater than the length of the third side

Mathematically represented as:

`\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \\ \\ a=8,b=10,c=9 \\ a+b>c\colon8+10>9\Rightarrow18>9(true) \\ a+c>b\colon8+9>10\Rightarrow17>9(true) \\ b+c>a\colon10+9>8\Rightarrow19>8(true) \\ \therefore8,10,9\text{ make a triangle} \end{gathered}`