The sides of the triangle are in the ratio 3: 4: 5 and its perimeter is 48cm.

The sides of the triangle are in the ratio 3: 4: 5 and its perimeter is 48cm. Find the perimeter of a triangle whose vertices are the midpoints of the sides of this triangle.

We denote the lengths of the sides of the triangle through 3 * x, 4 * x, 5 * x, then

3 * x + 4 * x + 5 * x = 48.

12 * x = 48.

X = 4.

Then the lengths of the sides are 3 * 4 = 12, 4 * 4 = 16, 5 * 4 = 20.

Since the vertices of the second triangle lie in the middle of the sides of the third triangle, they form midlines, the lengths of which are equal to half the length of the opposite base.

The lengths of the sides of the second triangle are equal: 12/2 = 6, 16/2 = 8, 20/2 = 10.

P = 6 + 8 + 10 = 24 cm.

Answer: The perimeter is 24 cm.