Answer:
x = 5 cm
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]AB^2+BC^2=AC^2[/tex]
We have
[tex]AB=8\ cm,\ BC=x\ cm,\ AC=\sqrt{89}\ cm[/tex]
Substitute:
[tex]8^2+x^2=(\sqrt{89})^2\qquad\text{use}\ (\sqrt{a})^2=a\ \text{for}\ a\geq0\\\\64+x^2=89\qquad\text{subtract 64 from both sides}\\\\x^2=25\to x=\sqrt{25}\\\\x=5\ cm[/tex]
