Find the ratio of the area of the rectangle to the area of the circle circumscribed about

Find the ratio of the area of the rectangle to the area of the circle circumscribed about it if the sides of the rectangle are 1: 4.

We enter the proportionality coefficient x and we get that the sides of the rectangle are equal to x and 4x.
By the Pythagorean theorem, we find the diagonal of the rectangle, which is the diameter of the circumscribed circle:
d = √ (x² + 16x²) = √17x² = x√17.
The radius of the circumscribed circle is half the diameter:
R = x√17 / 2.
We find the areas of the figures:
S pr. = X * 4x = 4x²;
S cr. = π * R² = π * (x√17 / 2) ² = 17πx² / 4.
We find the ratio of the area of the rectangle to the area of the circle:
S pr. / S cr. = 4x² / 17πx² / 4 = 16 / 17π = 16/17 * 3.14 = 16 / 53.38 = 0.2997377 ≈ 0.3.
Answer: the area ratio was 0.3.