Chapter 8 - Section 8.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 484: 85

$(10\sqrt{2}) \text{ } cm$

Using $a^2+b^2=c^2$ (or the Pythagorean Theorem), then \begin{array}{l}\require{cancel} x^2+x^2=20^2 \\\\ 2x^2=400 \\\\ x^2=\dfrac{400}{2} \\\\ x^2=200 \\\\ x=\sqrt{200} \\\\ x=\sqrt{100\cdot2} \\\\ x=\sqrt{(10)^2\cdot2} \\\\ x=10\sqrt{2} .\end{array} Hence, the legs measure $ (10\sqrt{2}) \text{ } cm .$