The length of the rectangle is 5 cm longer than the side of the square, and its width is 3 cm longer than the side of the square.

The length of the rectangle is 5 cm longer than the side of the square, and its width is 3 cm longer than the side of the square. find the perimeter of the rectangle if its area is 1.6 times the area of the square.

Let the side of the square be x cm, then the length of the rectangle is (x + 5) cm, and the width of the rectangle is (x + 3) cm.The area of ​​the square is x ^ 2 cm ^ 2, and the area of ​​the rectangle is (x + 5) (x + 3) cm ^ 2. By the condition of the problem, it is known that the area of ​​a rectangle is 1.6 times the area of ​​a square. To equalize the areas of the figures, you need to multiply the smaller area of ​​the square by 1.6 and it will become equal to 1.6x ^ 2 cm ^ 2 or (x + 5) (x + 3) cm ^ 2. Let’s make an equation and solve it.

1.6x ^ 2 = (x + 5) (x + 3);

1.6x ^ 2 = x ^ 2 + 3x + 5x + 15;

-1.6x ^ 2 + x ^ 2 + 8x + 15 = 0;

-0.6x ^ 2 + 8x + 15 = 0;

D = b ^ 2 – 4ac;

D = 8 ^ 2 – 4 * (-0.6) * 15 = 64 + 36 = 100; √D = 10;

x = (-b ± √D) / (2a);

x1 = (-8 + 10) / (2 * (-0.6)) = 2 / (- 1.2) <0 – side length cannot be negative;

x2 = (-8 – 10) / (- 1.2) = -18 / (- 1.2) = 15 (cm) – side of the square.

x + 5 = 15 + 5 = 20 (cm) – the length of the rectangle;

x + 3 = 15 + 3 = 18 (cm) – the width of the rectangle.

The perimeter of the rectangle is equal to the sum of the lengths of all sides. P = 2 (a + b) /

P = 2 (20 + 18) = 2 * 38 = 76 (cm).

Answer. 76 cm.