The ratio of the lengths of the sides of △abc is 3: 4: 6. the perimeter of the triangle whose vertices are the midpoints of the sides of △abc is 13 cm. find the lengths of the sides of △abc.

It is 6, 8, 12 , because you know that the perimeter of the smaller triangle is 13, and those are the midpoints of the larger triangle, so it is like half of the larger triangle. So, it happens that 3+4+6 = 13. So 3*2 , 4*2 , 6*2 will be your answer.