### Instruction: Two triangles are similar. The ratio of their areas is 1:4. If the height of the smaller triangle is 3 cm, how long is the corresponding height of the larger triangle, in centimeters?### Response: I know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides or heights.
So, if the ratio of the areas is 1:4, then the ratio of the heights is 1:2.
That means the larger triangle has a height that is twice as long as the smaller triangle's height.