The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (70 + 40) = 70 degrees.

The ratio of the perimeters of similar triangles is the same as the ratio of their corresponding sides, which is 1:5.

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2:3)² = 4:9.

By the Pythagorean theorem, if DE^2 + DF^2 = EF^2, then it is a right triangle. 6^2 + 8^2 = 36 + 64 = 100 = 10^2.

Using the Pythagorean theorem, hypotenuse = √(5^2 + 12^2) = √(25 + 144) = √169 = 13 cm.

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/4)^2 = 9/16.