Question

quadrilateral t is a scaled copy of quadrilateral
quadrilateral s
what is the value of r?
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Explanation:

Step1: Convert mixed numbers to improper fractions

$5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2}$, $4\frac{2}{5}=\frac{4\times5+2}{5}=\frac{22}{5}$

Step2: Find the scale factor

Since quadrilateral $T$ is a scaled - copy of quadrilateral $S$, the ratio of corresponding sides is the same. Let the scale factor be $k$. Then $k=\frac{4\frac{2}{5}}{5\frac{1}{2}}=\frac{\frac{22}{5}}{\frac{11}{2}}$

Using the rule for dividing fractions $\frac{a}{b}\div\frac{c}{d}=\frac{a\times d}{b\times c}$, we have $\frac{22}{5}\div\frac{11}{2}=\frac{22\times2}{5\times11}=\frac{44}{55}=\frac{4}{5}$

Step3: Calculate the value of $r$

We know that $r = 3\frac{1}{2}\times k$. Convert $3\frac{1}{2}$ to an improper fraction: $3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{7}{2}$

Then $r=\frac{7}{2}\times\frac{4}{5}$

Using the rule for multiplying fractions $\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$, we get $r=\frac{7\times4}{2\times5}=\frac{28}{10}=\frac{14}{5} = 2\frac{4}{5}$

Answer:

$2\frac{4}{5}$