Question

what is the value of p?
triangle n
triangle o is a scaled copy of triangle n.

Explanation:

Step1: Convert mixed numbers to improper fractions

$2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3}$, $2\frac{1}{5}=\frac{2\times5+1}{5}=\frac{11}{5}$, $4\frac{9}{10}=\frac{4\times10 + 9}{10}=\frac{49}{10}$

Step2: Find the scale factor

The scale factor $k$ is the ratio of corresponding sides. Let's assume the side of length $\frac{7}{3}$ in triangle $N$ corresponds to the side of length $\frac{49}{10}$ in triangle $O$. Then $k=\frac{\frac{49}{10}}{\frac{7}{3}}=\frac{49}{10}\times\frac{3}{7}=\frac{21}{10}$

Step3: Calculate the value of $p$

If the side of length $\frac{11}{5}$ in triangle $N$ corresponds to side $p$ in triangle $O$, then $p=\frac{11}{5}\times k$. Substitute $k = \frac{21}{10}$ into the formula: $p=\frac{11}{5}\times\frac{21}{10}=\frac{231}{50}=4\frac{31}{50}$

Answer:

$4\frac{31}{50}$