Question

What is the ratio of the length of to the length of?

Answer 1

1/4

Explanation:

Answer 2

1/4

Explanation:

What is the ratio of the length of to DE the length of BC

The perimeter of a sector is given by:

P =
`(\theta)/(360)**2\pi r`

Where
`\theta` is the angle it subtends from the center and r is the radius of the circle.

For Sector ADE, the radius (r) = r/2 and the angle
`\theta` = β. Therefore:

Perimeter of DE =
`(\beta)/(360)**2\pi ((r)/(2) )=(\beta)/(360)(\pi r)`

For Sector ABC, the radius (r) = r and the angle
`\theta` = 2β. Therefore:

Perimeter of BC =
`(2\beta)/(360)**2\pi r=(2\beta)/(360)(2\pi r)=(\beta)/(360)*(4\pi r)`

The ratio of the length of to DE the length of BC =