6. The circle has a circumference of 345cm. Line AC is the diameter of the circle. Square ABCD is made up of 4 equilateral triangles. What is the side length of side AB. Show your work for full marks. Remember. The image is not to scale.

Answer 1

To find the side length of side AB, we first need to find the radius of the circle.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

In this case, we have a circumference of 345 cm, so we can set up the equation as follows:

345 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 345 / (2π)

Next, we know that line AC is the diameter of the circle, which means it passes through the center of the circle. Since the square ABCD is made up of 4 equilateral triangles, and an equilateral triangle has all sides equal, we can conclude that line AC is the side length of each equilateral triangle.

Therefore, the side length of each equilateral triangle (and also side AB of the square) is equal to twice the radius. We can calculate this by multiplying the radius by 2:

2 * r = 2 * (345 / (2π))

Simplifying further:

2 * r = 345 / π

Thus, the side length of side AB is equal to 345 divided by π, which is approximately 109.901 cm.