The ratio of the lengths of the sides of a triangle abc is 3: 4: 6. m, n, and k are the midpoints of the sides. perimeter of the △mnk equals 5.2 in. find the length of the sides of the △abc. no picture.

Given that in a trianlgle the sides AB, BC, CA are in the ratio 3:4:6.

Let AB = 3k, BC = 4k and CA = 6k.

Then perimeter =3k+4k+6k = 13k

M, N, K are mid points of the sides.

By mid point theorem MN = 3k/2, NK = 4k/2 and KM = 6k/2

Hence perimeter of MNK = 13k/2 =5.2 (given)

Solve for k

k=2(5.2)/13 = 0.8

Hence sides are

AB = 3k = 3(0.8) = 2.4 in

BC = 4k= 3.2 in

CA = 4.8 in