In an isosceles triangle with a perimeter of 48 cm, the lateral side to the base is 5: 2. Find the sides of the triangle.

From geometry, we know that an isosceles triangle is called a triangle in which two sides are equal in length, where equal sides are called lateral, and the third side is the base.
We know from the problem statement that the perimeter of the triangle is 48 cm:
P = 48 cm.
It is also known that the lateral side refers to the base as 5: 2, that is, the lateral side consists of five equal parts and the base of two of the same parts. Then we can write the value of one part as a variable – x (cm).
Also, the perimeter of a triangle with sides abc, where a and b are the sides, and c is the base is the sum of the sides:
a + b + c = P
But we have an isosceles triangle, that is, a = b, which means that the second side also refers to the base as 5: 2.
Then we can write the equation for finding our perimeter:
10 * x + 2 * x = P
From this equation we find x, substituting the value of P = 48 cm.
12 * x = 48
x = 48/12 = 4 (cm)

Now, knowing x, we can find the value of all sides of the triangle:

a = b = 5 * x = 5 * 4 = 20 (cm)
c = 2 * x = 2 * 4 = 8 (cm)

Answer: 20 cm, 20 cm, 8 cm.