## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 7 - Similarity - 7-3 Providing Triangles Similar - Practice and Problem-Solving Exercises - Page 458: 51

#### Answer

The extremes are $15$ and $x$. The means are $x + 2$ and $9$. $x = 3$

#### 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, $a = 15$, $b = x + 2$, $c = 9$, and $d = x$. The extremes are $15$ and $x$. The means are $x + 2$ and $9$. Let's solve for $x$: $\frac{15}{x + 2} = \frac{9}{x}$ Use the cross products property to get rid of the fractions: $15x = 9(x + 2)$ Multiply on the right side of the equation to simplify: $15x = 9x + 18$ Subtract $9x$ from each side of the equation to move variables to the left side of the equation: $6x = 18$ Divide each side by $6$ to solve for $x$: $x = 3$

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