The rectangle represents a set of calculations that are common across all the given equations. Identify the calculations involved and solve the third equation on the same basis:

Correct option is D

36 : 81 = 6 : 9 : 15

The square roots of 36 and 81 are 6 and 9, respectively.

The third number in the ratio is 15, which is the sum of 6 and 9.

64 : 144 = 8 : 12 : 20

The square roots of 64 and 144 are 8 and 12, respectively.

The third number is 20, which is the sum of 8 and 12.

Applying the same logic to the third pair:

49 : 100

The square roots of 49 and 100 are 7 and 10, respectively.

The third number should be the sum of 7 and 10, which is 17.

Final Answer:

49 : 100 = 7 : 10 : 17