A sector of a circle has radius r r\,r cm and angle θ \theta\,θ radians, where 0<θ<π0 < \theta < \pi0<θ<π.
The perimeter of the sector is 20 cm and the area of the sector is 24 cm2^22.
Show that r r\,r satisfies the equation r2−10r+24=0r^2 - 10r + 24 = 0r2−10r+24=0.
Hence find the two possible pairs of values of r r\,r and θ\thetaθ.
State, with a reason, which of the two sectors has the longer arc.
225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.