Question

parallelogram f is a scaled copy of parallelogram e.
what is the value of d?

Explanation:

Step1: Convert mixed numbers to improper fractions

$2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}$，$2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{11}{4}$

Step2: Set up proportion

Since parallelogram $F$ is a scaled - copy of parallelogram $E$, the ratios of corresponding sides are equal. Let the ratio of the sides be $\frac{\text{side of }F}{\text{side of }E}$. We have the proportion $\frac{\frac{11}{4}}{\frac{11}{5}}=\frac{d}{5}$

Step3: Simplify the left - hand side of the proportion

$\frac{\frac{11}{4}}{\frac{11}{5}}=\frac{11}{4}\times\frac{5}{11}=\frac{5}{4}$

Step4: Solve for $d$

From $\frac{5}{4}=\frac{d}{5}$, cross - multiply gives $4d = 5\times5$，$4d=25$，$d=\frac{25}{4}=6\frac{1}{4}$

Answer:

$6\frac{1}{4}$