Question

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

Explanation:

Step1: Find the scale - factor

Since quadrilateral C is a scaled copy of quadrilateral B, we can find the scale - factor by comparing corresponding sides. Let's compare the sides with lengths $7\frac{1}{2}$ and $3\frac{3}{4}$. First, convert the mixed numbers to improper fractions. $7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{15}{2}$ and $3\frac{3}{4}=\frac{3\times4+3}{4}=\frac{15}{4}$. The scale - factor $k$ is given by the ratio of the side lengths of C to B, so $k=\frac{\frac{15}{4}}{\frac{15}{2}}=\frac{15}{4}\times\frac{2}{15}=\frac{1}{2}$.

Step2: Use the scale - factor to find $a$

We know that the side of length $8\frac{4}{5}$ in quadrilateral B corresponds to side $a$ in quadrilateral C. Convert $8\frac{4}{5}$ to an improper fraction: $8\frac{4}{5}=\frac{8\times5 + 4}{5}=\frac{44}{5}$. Then, since $a = k\times\frac{44}{5}$, and $k=\frac{1}{2}$, we have $a=\frac{1}{2}\times\frac{44}{5}=\frac{44}{10}=4\frac{2}{5}$.

Answer:

$4\frac{2}{5}$