Question

a designer created a kitchen floor tile in a triangular shape. two sides of the tile have lengths of 8 inches and 9 inches. what is the range of the possible lengths, (x), of the third side of the tile?

select the correct answer. for help, see this worked example.

• (8\text{ in} < x < 17\text{ in})
• (1\text{ in} < x < 17\text{ in})
• (x < 17\text{ in})
• (17\text{ in} < x < 1\text{ in})

Explanation:

State the given side lengths

Using the Triangle Inequality Theorem knowledge point
Given side lengths:

$$ a = 8\text{ in},\quad b = 9\text{ in} $$

Let the third side length be \(x\) inches.

Apply the triangle inequality bounds

Using the Triangle Inequality Theorem knowledge point

$$
LATEXBLOCK0
$$

Answer:

• (A) \(8\text{ in} < x < 17\text{ in}\)
• (B) \(1\text{ in} < x < 17\text{ in}\) (Correct answer)
• (C) \(x < 17\text{ in}\)
• (D) \(17\text{ in} < x < 1\text{ in}\)