Question

two sides of an acute triangle measure 5 inches and 8 inches. the length of the longest side is unknown. what is the greatest possible whole - number length of the unknown side? 13 inches 9 inches 8 inches 12 inches

Explanation:

Step1: Recall acute triangle rule

For an acute triangle with sides $a \leq b \leq c$, $a^2 + b^2 > c^2$.

Step2: Set up inequality

Let unknown side $c$ (longest), $a=5$, $b=8$.
$5^2 + 8^2 > c^2$
$\Rightarrow 25 + 64 > c^2$
$\Rightarrow 89 > c^2$

Step3: Solve for $c$

$c < \sqrt{89} \approx 9.43$

Step4: Find max whole number

Largest whole number less than 9.43 is 9.

Step5: Verify triangle inequality

$5+8>9$, $5+9>8$, $8+9>5$, which holds.

Answer:

B. 9 inches