Geometry: Common Core (15th Edition)

Published by Prentice Hall

Chapter 7 - Similarity - 7-3 Providing Triangles Similar - Practice and Problem-Solving Exercises - Page 458: 52

Answer

The extremes are $x - 3$ and $9$. The means are $x + 4$ and $5$. $x = 11.75$

Work Step by Step

A proportion takes the following form: $\frac{a}{b} = \frac{c}{d}$, where $a$ and $d$ are the extremes and $b$ and $c$ are the means. In this exercise, $a = x - 3$, $b = x + 4$, $c = 5$, and $d = 9$. The extremes are $x - 3$ and $9$. The means are $x + 4$ and $5$. Let's solve for $x$: $\frac{x - 3}{x + 4} = \frac{5}{9}$ Use the cross products property to get rid of the fractions: $5(x + 4) = 9(x - 3)$ Multiply to simplify: $5x + 20 = 9x - 27$ Subtract $9x$ from each side of the equation to move variables to the left side of the equation: $-4x + 20 = -27$ Subtract $20$ from each side of the equation to move constants to the right side of the equation: $-4x = -47$ Divide each side by $-4$ to solve for $x$: $x = 11.75$

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