Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 252: 38

Answer

48

Work Step by Step

The triangle in the upper left is a right triangle with a leg with a length of 3 and a hypotenuse with a length of 5. You may recognize this immediately as a 3-4-5 triangle, or you can use 3$^{2}$ + x$^{2}$ = 5$^{2}$ and solve for x. The rectangle had a width of 16, but when rearranging the pieces into a square the triangle we previously recognized as a 3-4-5 triangle will be removed, leaving a width of 12. This being a square, all sides are the same, so 4 sides with a length of 12 adds up to a total length of 48.
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