Question: A design for a circular garden is shown below.
The paths bordering Section 1 meet at a right angle.
The distance around the circular garden is 125.6 m.
Three paths of equal length run from the centre of the circle to the edge.
Section 2 and Section 3 have the same shape and area and are congruent
Landscape Design Plan
Design garden
Section 1
Shrub
Tree
Section 2
Path
Section 3
Flower
bed
Flower
bed
Flower
bed
Shrub
Question 22
What is the length of each path in the landscape design plan?
6.323 m
19.99 m
39.98 m
41.87 m
1. **State the problem:** We have a circular garden with circumference $125.6$ m.
Three paths of equal length run from the center to the edge, dividing the circle into three sections.
Section 1 is bordered by paths meeting at a right angle ($90^\circ$).
Sections 2 and 3 are congruent.
2. **Find the radius of the circle:**
The circumference formula is $$C = 2\pi r$$
Given $$C = 125.6$$, solve for $$r$$:
$$r = \frac{C}{2\pi} = \frac{125.6}{2 \times 3.14} = \frac{125.6}{6.28} = 20$$ m
3. **Analyze the angles:**
Section 1 has an angle of $90^\circ$.
The total circle is $360^\circ$.
Sections 2 and 3 are congruent, so their angles are equal.
Let each of these angles be $$x$$.
4. **Calculate the angles of Sections 2 and 3:**
$$90 + x + x = 360$$
$$2x = 360 - 90 = 270$$
$$x = \frac{270}{2} = 135^\circ$$
5. **Length of each path:**
The paths run from the center to the edge, so each path is a radius.
From step 2, the radius $$r = 20$$ m.
6. **Check the options:**
The radius is $20$ m, closest to $19.99$ m.
**Final answer:** The length of each path is approximately **$19.99$ m**.