# Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 20

3$\sqrt 2$

#### Work Step by Step

The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$ You are given the lengths of both legs as x and the length of the hypotenuse as 6. Substitute x in for a and b and 6 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $x^{2}$+$x^{2}$=$6^{2}$ 2$x^{2}$=36 Divide both sides by 2. $x^{2}$=18 Take the square root of both sides to find the length of the missing side. a=b=3$\sqrt 2$

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