Question

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 in < x < 17 in
1 in < x < 17 in
x < 17 in
17 in < x < 1 in

Explanation:

Step1: Apply the triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Here \(a = 8\) and \(b=9\).
First, calculate \(a + b\):
\(8+9=17\)

Step2: Calculate \(|a - b|\)

\(\vert8 - 9\vert=\vert- 1\vert = 1\)

Answer:

\(1\mathrm{in}\lt x\lt17\mathrm{in}\)