## Thinking Mathematically (6th Edition)

$x=8$ in.
RECALL: Two triangles are similar if: (1) corresponding angles are congruent (2) corresponding sides are proportional (i) Notice that the three pairs of corresponding angles are congruent. (ii) Notice also that the two pairs of corresponding sides are proportional. Thus, the two triangles are similar. Solve for the missing length using ratios to obtain: $\dfrac{18}{12} = \dfrac{12}{x}$ Cross-multiply to obtain: $18x=12(12) \\18x=144 \\x = \frac{144}{18} \\x=8$ Therefore, the missing length is $8$ inches.