Two roots, two geometries
8 written marks
A proper sector has perimeter \(26\) cm and area \(36\text{ cm}^2\).
Part a · 2 marks
Show that its radius satisfies \(r^2-13r+36=0\).
Part b · 3 marks
Find every possible radius-angle pair and check that each is a proper sector.
Part c · 3 marks
The sector is now known to be minor. Identify the valid pair, and find its arc length and disk-area fraction.
Complete-answer checking, worked solutions and indicative written criteria.
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