Question

here is a diagram with triangles abc and abc. if cb is 5, what is the length of bc? type your answer in the box. bc =

Explanation:

Step1: Determine similarity of triangles

Since $\angle A=\angle A$ and $\frac{AC'}{AC}=\frac{1.5}{1.5 + 4.5}=\frac{1.5}{6}=\frac{1}{4}$, $\frac{AB'}{AB}=\frac{2}{2 + 6}=\frac{2}{8}=\frac{1}{4}$, by the Side - Angle - Side (SAS) similarity criterion, $\triangle AC'B'\sim\triangle ACB$.

Step2: Use the property of similar - triangles

For similar triangles, the ratios of corresponding sides are equal. That is, $\frac{C'B'}{CB}=\frac{AC'}{AC}$. We know $C'B' = 5$, $AC'=1.5$, and $AC = 6$. Let $CB=x$. Then $\frac{5}{x}=\frac{1.5}{6}$.

Step3: Solve for $x$

Cross - multiply: $1.5x=5\times6$. So $1.5x = 30$. Then $x=\frac{30}{1.5}=20$.

Answer:

$20$