Question

Two similar trapezoids have areas of 49 cm2 and 9 cm2. find their similarity ratio.

Answer 1

Answer:  The required similarity ratio of the two trapezoids is $7:3.$

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

$\dfrac{\textup{area of first trapezoid}}{\textup{area of the second trapezoid}}=\dfrac{a^2}{b^2}\\\\\\\Rightarrow \dfrac{49}{9}=\dfrac{a^2}{b^2}\\\\\\\Rightarrow \left(\dfrac{a}{b}\right)^2=\left(\dfrac{7}{3}\right)^2\\\\\\\Rightarrow \dfrac{a}{b}=\dfrac{7}{3}\\\\\\\Rightarrow a:b=7:3.$

Thus, the similarity ratio of the two trapezoids is $7:3.$

Answer 2

The areas are 49 cm^2 and 9 cm^2.
The ratio of the areas is 49/9.
The ratio of the lengths of the sides is 7/3.
The similarity ratio is 7/3.