Question

6-107. examine the diagram below. the smaller triangle is similar to the larger triangle. write and solve a proportion to find x. it may be helpful to draw the two triangles separately.
hint: checkbox, with a checkmark on the first box

Explanation:

Step1: Identify corresponding sides

The vertical side of the larger triangle is $10+8=18$, and the vertical side of the smaller triangle is $8$. The horizontal side of the larger triangle is $8$, and the horizontal side of the smaller triangle is $x$. For similar triangles, the ratios of corresponding sides are equal.

Step2: Set up the proportion

$$\frac{x}{8} = \frac{8}{18}$$

Step3: Simplify and solve for $x$

First simplify $\frac{8}{18}$ to $\frac{4}{9}$, then multiply both sides by 8:
$$x = 8 \times \frac{4}{9} = \frac{32}{9}$$

Answer:

$\boldsymbol{\frac{32}{9}}$