Find the perimeter of the rectangle if it is known that the ratio of its sides is 7 and 2 and the area is 56 cm2.

From the condition it is known that the ratio of its sides is 7: 2, and the area of the rectangle is 56 cm ^ 2. And we need to find the perimeter of the rectangle.

Let us denote the similarity coefficient as k and write the sides of the rectangle as 7k and 2k.

Let’s apply the formula for finding the area of a rectangle:

S = a * b;

7k * 2k = 56;

14k ^ 2 = 56;

k ^ 2 = 4;

k = 2.

Now we can find the lengths of the sides of the rectangle: 7 * 2 = 14 cm and 2 * 2 = 4 cm.

P = 2 (a + b);

P = 2 (14 + 4) = 2 * 18 = 36 cm.

Answer: 36 cm perimeter of the rectangle.