Question

If ON = MN, find MN.

Answer 1

Use Pythagorean theorem.

[tex]|ON|^2+|MN|^2=|OM|^2\\\\x^2+x^2=8^2\\\\2x^2=64\ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=32\to x=\sqrt{32}\\\\x=\sqrt{16\cdot2}\\\\x=\sqrt{16}\cdot\sqrt2\\\\\boxed{x=4\sqrt2}

Answer: |MN| = 4√2.