Question

quadrilateral c is a scaled copy of quadrilateral b. what is the value of a?

Explanation:

Step1: Convert mixed numbers to improper fractions

$7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{15}{2}$, $3\frac{3}{4}=\frac{3\times4+3}{4}=\frac{15}{4}$, $9\frac{4}{5}=\frac{9\times5 + 4}{5}=\frac{49}{5}$, $4\frac{9}{10}=\frac{4\times10+9}{10}=\frac{49}{10}$.

Step2: Find the scale factor

The scale factor $k$ is the ratio of corresponding sides. Using the pair of known - side lengths: $k=\frac{\frac{15}{4}}{\frac{15}{2}}=\frac{15}{4}\times\frac{2}{15}=\frac{1}{2}$.

Step3: Calculate the value of \(a\)

Let the side length in quadrilateral \(B\) be \(x = 8\frac{4}{5}=\frac{44}{5}\). Since \(a=k\times x\), substituting \(k = \frac{1}{2}\) and \(x=\frac{44}{5}\), we get \(a=\frac{1}{2}\times\frac{44}{5}=\frac{22}{5}=4\frac{2}{5}\).

Answer:

\(4\frac{2}{5}\)