The figure below shows the shape of a flower bed. If arc QR is a semicircle and PQRS a rectangle with QR > RS, what is the perimeter of the flower bed?

I. The perimeter of rectangle PQRS is 28 feet.
II. Each diagonal of rectangle PQRS is 10 feet long.

Let's take the length of the side of rectangles to be a and b, respectively, such that a>b

Once we find a, we can also find the perimeter of the semi-perimeter since the radius of the semi-circle would be (a/2)

Using statement 1 alone:
This statement gives us that 2(a+b)=28; since we can not find the value of a or b alone, we can not determine the perimeters of the flower bed

Using statement 2 alone:

We get that $$a^2+b^2=100$$, which alone is insufficient in finding the values of $$a$$ and $$b$$. 

Using both statements together, we get the following:

$$a+b=14$$ and $$a^2+b^2=100$$
Using the formula, $$\left(a+b\right)^2=a^2+b^2+2ab$$, we can get the value of $$ab$$.
And using these, we can get the value of a-b through
$$\left(a-b\right)^2=\left(a+b\right)^2-4ab$$

Once we have a+b and a-b, we can find the values of a and b individually. 

Thus, with both statements taken together, the perimeter can be determined. 

Therefore, Option C is the correct answer.