Question

what is the value of X? show all of your work

Answer 1

Answer:

x = 5 cm

Step-by-step explanation:

Use the Pythagorean theorem:

$AB^2+BC^2=AC^2$

We have

$AB=8\ cm,\ BC=x\ cm,\ AC=\sqrt{89}\ cm$

Substitute:

$8^2+x^2=(\sqrt{89})^2\qquad\text{use}\ (\sqrt{a})^2=a\ \text{for}\ a\geq0\\\\64+x^2=89\qquad\text{subtract 64 from both sides}\\\\x^2=25\to x=\sqrt{25}\\\\x=5\ cm$