Final answer:
After calculating the value of one part of the ratio as 15 cm, the height of the smallest sister, corresponding to the smallest ratio, is found to be 45 cm.
Step-by-step explanation:
The question involves finding the height of the smallest sister when the sum of heights of three sisters is 180 cm and their heights are in the ratio of 4:3:5. To solve this, we first add up the parts of the ratio: 4 + 3 + 5 = 12 parts in total. Then, we calculate the value of one part by dividing the total height by the number of parts: 180 cm ÷ 12 parts = 15 cm per part. Since the heights are in the ratio 4:3:5, the shortest sister, which corresponds to 3 parts, would have a height of 3 parts × 15 cm per part = 45 cm. Hence, the height of the smallest sister is 45 cm, which corresponds to option c.