Select the option in which the numbers are related in the same way as are the numbers of the following sets.
(2, 4, 36)
(4, 6, 100)

Solution

(2, 4, 36)

Third number = $$\left(first\ number+second\ number\right)^2$$

= $$\left(2+4\right)^2$$

= $$\left(6\right)^2$$

= 36

(4, 6, 100)

Third number = $$\left(first\ number+second\ number\right)^2$$

= $$\left(4+6\right)^2$$

= $$\left(10\right)^2$$

= 100

Option (a) (8, 4, 1020)

Third number = $$\left(8+4\right)^2$$

= $$\left(12\right)^2$$
= 144
The above-given logic is not applicable here. So this is not the correct answer.

Option (b) (12, 4, 230)

Third number = $$\left(12+4\right)^2$$

= $$\left(16\right)^2$$
= 256
The above-given logic is not applicable here. So this is not the correct answer.

Option (c) (4, 4, 64)

Third number = $$\left(4+4\right)^2$$

= $$\left(8\right)^2$$
= 64
The above-given logic is applicable here. So this is the correct answer.

Option (d) (14, 2, 75)

Third number = $$\left(14+2\right)^2$$

= $$\left(16\right)^2$$

= 256

The above-given logic is not applicable here. So this is not the correct answer.