Find the perimeter of a rectangle inscribed in a circle with a radius of 5.7 cm if the sides of the rectangle are 3: 4

We know that the sides of the rectangle are 3: 4, we also know that the rectangle is inscribed in a circle with a radius of 5.7 cm.To calculate the perimeter of the rectangle, we use the formula:

P = 2 (a + b).

The radius of the circle is half the diagonal of the rectangle. Consider a right-angled triangle formed by the sides of a rectangle (legs) and a diagonal (hypotenuse).

The diagonal is 5.7 * 2 = 11.4 cm.

3x and 4x are legs and apply the Pythagorean theorem:

9x ^ 2 + 16x ^ 2 = 129.96;

25x ^ 2 = 129.96;

x ^ 2 = 5.1984;

x = 2.28.

3 * 2.28 = 6.84 and 4 * 2.28 = 9.12.

P = 2 (6.84 + 9.12) = 2 * 15.96 = 31.92 cm perimeter.