Question
Sides of two similar triangles are in the ratio 4:9. What will be ratio of
areas of these triangles ?
areas of these triangles ?
Answers
GPT-4o mini
If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Given that the sides of the two triangles are in the ratio of 4:9, we can find the ratio of their areas as follows:
\[
\text{Ratio of areas} = \left(\frac{\text{Side 1}}{\text{Side 2}}\right)^2 = \left(\frac{4}{9}\right)^2 = \frac{16}{81}
\]
Thus, the ratio of the areas of the two similar triangles is \(16:81\).
\[
\text{Ratio of areas} = \left(\frac{\text{Side 1}}{\text{Side 2}}\right)^2 = \left(\frac{4}{9}\right)^2 = \frac{16}{81}
\]
Thus, the ratio of the areas of the two similar triangles is \(16:81\).