Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 1, Equations and Inequalities - 1.6 Solve Inequalities - 1.6 Exercises - Mixed Review - Page 47: 71

Answer

$x=12$ Side lengths: $2x-2=15$ $x-2=10$

Work Step by Step

The perimeter is the sum of the length of all sides. This rhombus has two sides with a length of $2x-9$ each and two sides with a length of $x-2$ each, therefore: $Perimeter=50=2(2x-9)+2(x-2)$ Apply the distributive property: $50=4x-18+2x-4$ Group the terms with x as a common factor: $50=(4+2)x-18-4$ Do the additions: $50=6x-22$ Add 22 to each side of the equation: $72=6x$ Divide both sides by 6: $x=12$ The side lengths are then: $2x-2=2\cdot12-9=24-9=15$ $x-2=12-2=10$
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