University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 13: 71



Work Step by Step

The perimeter of the given isosceles right triangle with equal sides measuring $\:x\:$ and hypotenuse $\:h\:$ is $\:2x+h.$ Apply the pythagorean theorem to get the length of equal sides in terms of $\:h.$ $x^2+x^2=h^2$ $\Rightarrow\: x=\frac{h}{\sqrt{2}}=\frac{h\sqrt{2}}{2}$ So, the perimeter of the triangle becomes: $=\:2\cdot(\frac{h\sqrt{2}}{2})+h=h\sqrt{2}+h$ The function for the cost of fencing would be: $C=5\cdot h\sqrt{2}+10\cdot h$ $C=5h(\sqrt{2}+2)$
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