If the ratio of the areas of two similar triangles is 25:16, then the ratio of their perimeters will be -

For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides, and therefore also to the square of the ratio of their perimeters. Taking the square root of the area ratio $25:16$ gives the perimeter ratio $\sqrt{25}:\sqrt{16} = 5:4$.