The sides of a triangle are 48 cm, 24 cm, 56 cm.Find the perimeter of a triangle similar to this one if its largest side is 7 cm.

To solve the problem, you first need to determine exactly how the largest side of the first triangle relates to the largest side of the second triangle.

Since the largest side is 56 cm, we get:

56/7 = 8: 1.

In this case, the other two sides of the triangle will also be 1: 8.

In this case, we get:

48/8 = 6 cm.

24/8 = 3 cm.

In order to determine the perimeter of such a triangle, you need to add up all the sides.

We get:

7 + 6 + 3 = 16 cm.

Solving the problem through the perimeter relation
Since, by the problem statement, we know that the largest sides of the triangles are related as:

56: 7 = 8: 1, their sides have a similar ratio, where:

Р1 – perimeter of the first triangle;
P2 is the perimeter of the second triangle;
a1, b1, c1 – sides of the first triangle;
a2, b2, c2 – sides of the second triangle.
We get equality, in which:

1: 8 = P2: P1.

We paint the perimeter of the first triangle as the sum of the sides.

1: 8 = P2: (56 + 48 + 24).

1: 8 = P2: 128.

P2 = 128/8.

P2 = 16 cm.

Answer: The perimeter of the triangle is 16 cm.