Question 9.2E2: Similar Figures Consider the similar figures in Fig. 9.21. D......

a)  We will represent the length of side \overline{BC} with the variable x. Because the corresponding sides of similar figures must be in proportion, we can write a proportion (as explained in Section 6.2) to determine the length of side \overline{BC}. Corresponding sides \overline{CD} and \overline{RS} are known, so we use them as one ratio in the proportion. The side corresponding to \overline{BC} is \overline{QR}.

\frac{BC}{QR}  =  \frac{CD}{RS}
\frac{x}{3}  =  \frac{3}{4.5}

Now we solve for x.

x  ⋅  4.5  =  3  ⋅  3
4.5x  =  9
x  =  2

Thus, the length of side \overline{BC} is 2 units.

b)  We will represent the length of side \overline{PQ} with the variable y. The side corresponding to \overline{PQ} is \overline{AB}. We will work part (b) in a manner similar to part (a).

\frac{PQ}{AB }  =  \frac{RS}{CD}
\frac{y}{4}  =  \frac{4.5}{3}
y  ⋅  3  =  4  ⋅  4.5
3y  =  18
y  =  6

Thus, the length of side \overline{PQ} is 6 units.