if the ratio between the perimeters of two similiar triangles is 4:9 , then the ratio between their two surface areas =

1 answer

The ratio between the perimeters of two similar triangles is equal to the ratio between their sides. Therefore, if the ratio between the perimeters is 4:9, then the ratio between the sides of the two triangles is also 4:9.

Since the surface area of a triangle is proportional to the square of its side length, we can square the ratio between the sides to find the ratio between their surface areas.

(4:9)^2 = 16:81

Therefore, the ratio between the surface areas of the two similar triangles is 16:81.