A sector of a circle has radius $r\,$ cm and angle $\theta\,$ radians, where $\theta < \pi$ .

The perimeter of the sector is 20 cm and the area of the sector is 24 cm $^2$ .

Show that $r\,$ satisfies the equation $r^2 - 10r + 24 = 0$ .

Hence find the two possible pairs of values of $r\,$ and $θ\theta$ .

State, with a reason, which of the two sectors has the longer arc.

A sector of a circle has radius $r\,$ cm and angle $\theta\,$ radians, where $\theta < \pi$ .

The perimeter of the sector is 20 cm and the area of the sector is 24 cm $^2$ .

Show that $r\,$ satisfies the equation $r^2 - 10r + 24 = 0$ .

Hence find the two possible pairs of values of $r\,$ and $θ\theta$ .

State, with a reason, which of the two sectors has the longer arc.

1 Pure Mathematics

1 Pure Mathematics Questions