SPM 2022 Add Maths Paper 1, Question 12Progressions

12 Diagram 8 shows a purple-coloured right-angled triangle pattern on the net of a rectangular roll of paper (the rectangle is 12 cm tall and the triangles increase in size from left to right). It is given that the length of the base of the first triangle is a cm and the length of each subsequent base increases by d cm. (a) Derive that the length of the base of the n-th triangle is T_n = a + (n − 1)d.

12 (b) On the net, the 31st purple-coloured triangle is the last triangle with an area of 72 cm² and it is given that a = 30d. (i) Find the value of d, in cm.

12 (b)(ii) Zul wants to send a number of rolls of the paper to his friend through a courier company. Table 2 shows the delivery charges: mass 0 to 2.5 kg costs RM9.00, and every subsequent 500 g costs RM1.20. If Zul has RM15 and the mass of the paper per cm² is 4 × 10^(−5) kg, calculate the maximum number of rolls of the paper that can be sent. [a = 30d, d = 0.2 cm, 31 triangles]