Question

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

Answer 1

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.

Answer 2

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

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

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