The perimeter of the rectangle is 52 cm, and its sides are 4: 9 find the area of the rectangle.

The perimeter of the rectangle is 52 cm, and its sides are 4: 9 find the area of the rectangle. Find the area of the square whose perimeter is equal to the perimeter of the rectangle.

1. If one side of the rectangle is “4X”, then the other will be “9X”. The formula for the perimeter of a rectangle can be formulated as P = 2 * (a + b). Let’s compose and solve the equation:

52 = 2 * (4X + 9X);

13X = 26;

X = 2.

2. Find the sides of the rectangle:

a = 4 * 2 = 8 (cm);

b = 9 * 2 = 18 (cm).

3. Let’s calculate the area of a rectangle with these sides:

S = a * b = 8 * 18 = 144 (cm2).

4. Find the side of the square if its perimeter is 52 cm:

P = 4a = 52;

a = 52/4;

a = 13 (cm).

5. Calculate the area of a square with a side of 13 cm:

S = a2 = 132 = 169 (cm2).

Answer: the area of the rectangle is 144 cm2, the area of the square is 169 cm2.