1. We are given two similar rectangles. The dimensions of the first rectangle are 8 cm by 12 cm. 2. Since the rectangles are similar, their corresponding sides are proportional. 3. The perimeter of the first rectangle is $2(8 + 12) = 2 \times 20 = 40$ cm. 4. The perimeter of the second rectangle is given as 150 cm. 5. Let the length of the second rectangle be $L$ cm and the width be $W$ cm. 6. Since the rectangles are similar, the ratio of the lengths equals the ratio of the widths. 7. The ratio of the perimeters will also be the same as the ratio of corresponding sides. 8. This means $\frac{150}{40} = \frac{L}{8} = \frac{W}{12}$. 9. Simplify $\frac{150}{40} = \frac{15}{4}$. 10. So, $L = 8 \times \frac{15}{4} = 8 \times 3.75 = 30$ cm. 11. Therefore, the length of the second rectangle is 30 cm. Final answer: (b) 30