The perimeter of the triangle is 51 cm. The ratio of the length of the first side to the length of the third is 1: 2.

The perimeter of the triangle is 51 cm. The ratio of the length of the first side to the length of the third is 1: 2. The ratio of the length of the second side to the length of the third is 3: 4. Find the number of parts.

Let CMR be a given triangle, the perimeter P (CMR) is 51 cm. CM refers to MR as 1 to 2, MR refers to KR as 3 to 4.
Let MP be equal to 3x, and KP is 4x (since MR: KP = 3: 4). Then KM = 1.5x (since KM: MR = 1: 2, that is, KM is half the MR).
Let us express the perimeter of the CMR triangle:
P (KMP) = KM + MR + KP = 51.
The equation turns out: 1.5x + 3x + 4x = 51.
8.5x = 51.
x = 51: 8.5.
x = 6.
Hence KM = 1.5 * 6 = 9 cm, MR = 3 * 6 = 18 cm, KR = 4 * 6 = 24 cm.