The area of a rectangle is length multiplied by breadth. For breadths 12 cm, 10 cm and 8 cm, the areas are 156 square cm, 130 square cm and 104 square cm respectively. The linear pattern is 13b.
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The fare for the first 2 km is 25 rupees. After that, the fare increases by 15 rupees per km. For 10 km, the extra distance is 8 km. Therefore, the total fare is 145 rupees.
Bela starts with 100 rupees and spends 5 rupees daily. Let the number of days be x. Then 100 minus 5x equals 40. Solving gives x equal to 12. Therefore, she will have 40 rupees after 12 days.
The pattern increases by 2 squares at every stage. The next three stages after Stage 4 will have 9, 11 and 13 squares. Therefore, the sequence up to Stage 7 is 1, 3, 5, 7, 9, 11, 13.
Let the integers be 2x and 5x because their ratio is 2:5. Their difference is 63. Therefore, 5x minus 2x equals 63. Solving gives x equal to 21. Hence, the integers are 42 and 105.