Question

triangle o is a scaled copy of triangle n.
triangle n has a side labeled 3\\(\frac{1}{2}\\) and another side labeled 5\\(\frac{1}{2}\\). triangle o has a side labeled 4\\(\frac{9}{10}\\) and another side labeled p.
what is the value of p?

Explanation:

Step1: Convert mixed numbers to improper fractions

$3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}$, $4\frac{9}{10}=\frac{4\times10+9}{10}=\frac{49}{10}$, $5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2}$

Step2: Find the scale factor

The scale factor $k$ is the ratio of the corresponding sides of the two similar triangles. So $k=\frac{\frac{49}{10}}{\frac{7}{2}}=\frac{49}{10}\times\frac{2}{7}=\frac{7}{5}$

Step3: Calculate the value of $p$

Since $p = 5\frac{1}{2}\times k$, substitute $k = \frac{7}{5}$ and $5\frac{1}{2}=\frac{11}{2}$ into the formula. Then $p=\frac{11}{2}\times\frac{7}{5}=\frac{77}{10}=7.7$

Answer:

$7.7$