Question

two sides of an obtuse triangle measure 9 inches and 14 inches. the length of longest side is unknown. what is the smallest possible whole - number length of the unknown side? 16 inches 25 inches 17 inches 24 inches

Explanation:

Step1: Recall triangle inequality rule

For sides $a,b,c$, $a+b>c$, $a+c>b$, $b+c>a$. Here, let unknown side be $x$ (longest side, so $x>14$).

Step2: Recall obtuse triangle condition

For longest side $x$, $x^2 > 9^2 + 14^2$
Calculate $9^2 + 14^2 = 81 + 196 = 277$

Step3: Find smallest integer $x$

Find smallest integer $x>14$ where $x^2>277$.
$16^2=256<277$, $17^2=289>277$
Check triangle inequality: $9+14=23>17$, which holds.

Answer:

17 inches