ABCD is a trapezium with AB parallel to DC. DC = 15 cm and AB = x cm. The perpendicular distance between AB and DC is 3 cm less than the length of AB. The area of ABCD is 75 cm². Show that x² + 12x – 195 = 0.

1. (a)(i)ABCD is a trapezium with AB parallel to DC. DC = 15 cm and AB = x cm. The perpendicular distance between AB and DC is 3 cm less than the length of AB. The area of ABCD is 75 cm². Show that x² + 12x – 195 = 0.[2]
2. (a)(ii)Find AB, giving your answer correct to 1 decimal place.[3]
3. (a)(iii)AD is 0.8 cm longer than BC. Given that the perimeter of the trapezium is 38.0 cm, calculate AD.[2]
4. (b)(i)Another trapezium, LMNO, has LM parallel to ON. The reflex angle LMN = 252°. Calculate ∠MNO.[2]
5. (b)(ii)The ratios of the angles inside the trapezium are LÔN : LMN=1:2 and OLM : MÑO=1:k. Find k, giving your answer as a fraction in its simplest form.[3]

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