Explanation:

Let the length of the rectangle be L cm and the breadth be B cm.
Area of the rectangle = 48 cm²
∴   L × B = 48
Also, the diagonal of the rectangle will coincide with a diamter of the circle, because the angle in a semicircle will be a right angle.
As all four angles of a rectangle are right angles, the diagonals of the rectangle must also be diameters of the circle.
∴ Diagonal of a rectangle = 2 × R = 10 cm
Now, the diagonal of a rectangle = √L² + B²
∴ L² + B² = 100
We know that L² + B² = 100 and that L × B = 48
∴ L² + B² + 2 × L × B = 100 + 2 × 48 = 196 = (L + B)²
The positive root of (L + B) is therefore √196 = 14cm
∴   The perimeter of the rectangle is equal to 2 × (L + B) = 28 cm