Question

Find the missing length . Leave your answers in simplest radical form

Answer 1

Use the Pythagorean theorem:

2)

$x^2+7^2=14^2\\\\x^2+49=196\qquad\text{subtract 49 from both sides}\\\\x^2=147\to x=\sqrt{147}\\\\x=\sqrt{49\cdot3}\\\\x=\sqrt{49}\cdot\sqrt3\\\\\boxed{x=7\sqrt3\ mi}$

4)

$x^2+9^2=(\sqrt{226})^2\\\\x^2+81=226\qquad\text{subtract 81 from both sides}\\\\x^2=145\to \boxed{x=\sqrt{145}\ km}$