2. A new local park is about to be built. However. before the park can be constructed, the city wl APPLICATION - CONTINUED eed to determine the perimeter of SOUARE PORS. The only known dimension/info is as follows: (a) Point "O" is the centre of the circle. (b) Line "OS" and line "OT" are both radii of the circle. (c) The circumference of the circle is 220cm.
What is the perimeter of square PQRS? Show ALL of your work for full marks.[
To find the perimeter of square PQRS, we need to determine the length of one side of the square.
Given that line OS and line OT are radii of the circle, we know that they are equal in length. Let's call the length of each radius r.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is 220 cm. Therefore, we can write:
220 cm = 2πr
To find r, we can rearrange the equation:
r = 220 cm / (2π)
Now, we can calculate the value of r:
r ≈ 220 cm / (2 × 3.14)
r ≈ 220 cm / 6.28
r ≈ 35.03 cm
Since OS and OT are both radii of the circle, they have a length of approximately 35.03 cm.
Now, let's consider square PQRS. Each side of the square will have the same length as OS and OT.
Therefore, the perimeter of square PQRS will be:
Perimeter = 4 × Length of one side
Perimeter = 4 × 35.03 cm
Perimeter ≈ 140.12 cm
Therefore, the perimeter of square PQRS is approximately 140.12 cm.