Answer: The required similarity ratio of the two trapezoids is [tex]7:3.[/tex]
Step-by-step explanation: Given that the areas of two similar trapezoids are 49 cm² and 9 cm².
We are to find the similarity ratio of the two trapezoids.
The similarity ratio of two trapezoids will be the ratio of the lengths of their corresponding sides.
Let, a cm and b am be the lengths of the corresponding sides of the two trapezoids.
Then, we know that
[tex]\dfrac{\textup{area of first trapezoid}}{\textup{area of the second trapezoid}}=\dfrac{a^2}{b^2}\\\\\\\Rightarrow \dfrac{49}{9}=\dfrac{a^2}{b^2}\\\\\\\Rightarrow \left(\dfrac{a}{b}\right)^2=\left(\dfrac{7}{3}\right)^2\\\\\\\Rightarrow \dfrac{a}{b}=\dfrac{7}{3}\\\\\\\Rightarrow a:b=7:3.[/tex]
Thus, the similarity ratio of the two trapezoids is [tex]7:3.[/tex]
