The area of the patio is : 20 x 14 = 280 (ft²)

There are 2 cases (because there's no figure) :

+ The garden is tangent to 2 20-ft sides and 1 14-ft side

The radius of the garden is : \(14:2=7\left(ft\right)\)

The area of the garden is : \(7^2\pi=49\pi\left(ft^2\right)\) 

The answer is : \(\dfrac{100\left(280-49\pi\right)}{280}\%\approx45\%\)

+ The garden is tangent to 2 14-ft sides and 1 20-ft side

The radius of the garden is : \(20:2=10\left(ft\right)\)

The area of the garden is : \(10^2\pi=100\pi\left(ft^2\right)\) (asburd because \(100\pi>280\))

So, the answer is 45%