Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 6 - Polygons and Quadrilaterals - 6-4 Properties of Rhombuses, Rectangles, and Squares - Practice and Problem-Solving Exercises - Page 380: 38


$x = 3$ All sides must have a length of $15$.

Work Step by Step

All sides of a rhombus are congruent, so let us take two of the sides and set them equal to one another so we can find the value of one of the variables: $4x + 3 = 15$ Subtract $3$ from each side of the equation to move constants to the right side of the equation: $4x = 12$ Divide each side of the equation by $4$ to solve for $x$: $x = 3$ Now, we set the two other opposite sides equal to one another: $3y = 5x$ Plug in $3$ for $x$: $3y = 5(3)$ Multiply to simplify: $3y = 15$ Divide each side by $3$ to solve for $y$: $y = 5$ If this is a rhombus, then all sides are congruent; therefore, we can deduce that all sides must have a length of $15$, which is given as the length of one of the sides.
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