The diagonals of a rectangle are 2 and 16 cm larger than its sides, respectively.

The diagonals of a rectangle are 2 and 16 cm larger than its sides, respectively. Find the area of the rectangle and the area of the square, the perimeter of which is equal to the perimeter of the rectangle.

The diagonal and the two sides of the rectangle form a right-angled triangle. Let’s denote the smaller side through x and write down the Pythagorean formula.

x ^ 2 + (x + 14) ^ 2 = (x + 16) ^ 2;

x ^ 2 + x ^ 2 + 14 * x + 14 * x + 196 = x ^ 2 + 16 * x + 16 * x + 256;

x ^ 2 – 4 * x – 60 = 0;

D = 16 + 240 = 256;

x1 = (4 + 16) / 2 = 10;

x2 = (4 – 16) / 2 = -6 (the leg cannot be negative);

The sides of the rectangle are 10 cm and 24 cm. The area of the rectangle is:

Spr = 10 * 24 = 240 cm ^ 2;

Perimeter of the rectangle: 10 + 24 + 24 + 10 = 68 cm.

Side of a square with the same perimeter: 68: 4 = 17 cm.

The area of this square is 17 * 17 = 289 cm ^ 2.