Question

Giver DABC ~0872, find the ratio and the missing sicles, 12 m 21m B Im А 모드 Z с C 근 SZ b Z 17.5m be Z-

Answer 1

b = 10.03, z= 12.25

1) Similar triangles have proportional sides and congruent angles. Therefore we can write out the following ratios:

$\begin{gathered} \frac{BC}{YZ}=\frac{CA}{XZ} \\ \frac{12}{21}=\frac{b}{17.5} \\ 21b=12\cdot17.5 \\ \frac{21b}{21}=\frac{12}{21}\cdot\frac{17.5}{21} \\ b=10.03 \end{gathered}$

2) And for the other missing side, we can write out this proportion:

$\begin{gathered} \frac{BC}{AB}=\frac{ZY}{XY} \\ \frac{12}{7}=\frac{21}{z} \\ 12z=7\cdot21 \\ \frac{12z}{12}=\frac{7\cdot21}{12} \\ z=12.25 \end{gathered}$

3) Hence, the missing sides are b = 10.03 (rounded off to the nearest hundredth) and z= 12.25