# Chapter 6 - Section 6.4 - Square Roots and the Pythagorean Theorem - Exercise Set - Page 445: 38

15 units

#### Work Step by Step

In the given right triangle, both legs are given and the hypotenuse is missing. Leg$_{1}$=9 and Leg$_{2}$=12 In order to find the hypotenuse, the Pythagorean theorem must be applied: $a^{2}$+$b^{2}$=$c^{2}$ Replace $a$ the value of Leg$_{1}$ and $b$ with the value of Leg$_{2}$. Let $c$ represent the hypotenuse. $9^{2}$+$12^{2}$$=$$c$$^{2} 81+144$$=$$c$$^{2}$ (work out the squares) $225$$=$$c$$^{2} (add) \sqrt 225$$=$$\sqrt c$$^{2}$ (square root both sides to cancel the square on $c$) $15=c$ Since $c$ represents the hypotenuse, then the hypotenuse$=15$ units (no unit of measurement is given, so "units" are used).

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