Question

The ratio of the perimeters of two similar triangles is 3:7. Find the ration of the areas! Please help, I am really not sure. And please explain well in terms that I can understand and draw a visual as well.

Answer 1

I don't have a visual I can provide, but the ratio of the areas is the square of the ratio of the perimeters of a 2D figure.

Intuitively, you can imagine that the triangle is simply being "scaled up" by a factor of 7/3, so the base scales up to 7/3 its original length and the height becomes 7/3 its original height.

Therefore, the new ratio is the square of the ratio of the perimeters, which is 9:49.