Questions: CP'/CP

Transcript text: $\frac{C P^{\prime}}{C P}$

Solution

Solution Steps

Step 1: Find the ratio of CP' to CP

The ratio of corresponding sides in similar figures is constant. We're given that the ratio $\frac{CP'}{CP}$ is the scale factor. From the figure, we have $CP = 8+4 = 12$. Also $CP' = 12.5 + y$.

Step 2: Find the scale factor

The ratio of corresponding sides $\frac{P'}{P}$ in the larger triangle to the smaller triangle is $\frac{12.5}{5} = \frac{5}{2} = 2.5$.

Step 3: Calculate y

Since the ratio $\frac{CP'}{CP}$ is equal to the scale factor, we have $\frac{12.5 + y}{12} = \frac{5}{2}$. So, $2(12.5+y) = 12 * 5$, which simplifies to $25 + 2y = 60$. Therefore, $2y = 35$ and $y = 17.5$.

Step 4: Calculate x

Similarly, the ratio of corresponding sides must be equal, hence, $\frac{x}{4} = \frac{5}{2}$, or $2x = 20$, hence $x = 10$.