Question

Pls help it due soon.
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Answer 1

`\mathrm{D.\:}14<x<32`

Explanation:

In any triangle, the sum of any two sides must be greater than the other side. Therefore, in the given triangle with side lengths
`9` and
`12`, we can write the following inequalities:

`\begin{cases}(x-2)+9>21,\\21+9>(x-2)\\\end{cases}`

Solving these inequalities, we get:

`x-2>12,\\x>14\\\\30>x-2,\\x<32`.

Combining this into one inequality gives us:

`\mathrm{D.\:}14<x<32`.