'n Landskapskuns-tiaan beplan om blomme binne twee konsentris-sirkels rondom 'n vertikale lamppaal PQ te plant - NSC Mathematics - Question 7 - 2020 - Paper 2

The area of the flower garden can be represented as the difference between the areas of the outer and inner circles:

$\text{Area} = \pi (3r)^2 - \pi r^2 = 9\pi r^2 - \pi r^2 = 8\pi r^2.$

Thus, the area is:

$\text{Area} = 8\pi r^2$

Using the cosine rule in triangle RSP, we can express RS as follows:

$RS^2 = r^2 + (3r)^2 - 2(r)(3r)\cos 2x$

Which simplifies to:

$RS^2 = r^2 + 9r^2 - 6r^2\cos 2x$

Thus,

$RS^2 = r^2(1 - 6\cos 2x)$

Therefore,

$RS = \frac{r}{\sqrt{10 - 6\cos 2x}}$

To find RS, substitute r and x into the equation derived in the previous step:

$RS = \frac{10}{\sqrt{10 - 6\cos(56°)}}$

Calculating:

$RS \approx 35 m$