Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 241: 29

Answer

$MN=4$

Work Step by Step

Using the Pythagorean Theorem we can find the length of $AC$. $a^{2}+b^{2}=c^{2}$ Remember, the hypotenuse is always the longest side, or the side opposite the right angle, in this case $AB$. $AC^{2}+CB^{2}=AB^{2}$ $a^{2}+ 15^{2}=17^{2}$ Simplify... $a^{2}+225=289$ Subtract 225 from both sides... $a^{2}=64$ Square root both sides... $a=8$ OR $AC=8$ $MN$ is the mid-segment of $\triangle ABC$. A triangle's mid-segment is half the length of the parallel side. If $AC=8$, then $MN$ equals half that length or, $MN=4$.
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