f 14 is one member of a Pythagorean triplet, which of the following is the triplet?*a) 13,14.15b) 14, 15,16c) 7, 48, 50d)14,48, 50

A Pythagorean triplet is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2.

Given that 14 is one member of the triplet, we need to find the set where 14^2 (which is 196) plus the square of another number equals the square of the third number.

Let's check each option:

a) 13, 14, 15: 13^2 + 14^2 = 169 + 196 = 365, which is not equal to 15^2 (225). So, this is not a Pythagorean triplet.

b) 14, 15, 16: 14^2 + 15^2 = 196 + 225 = 421, which is not equal to 16^2 (256). So, this is not a Pythagorean triplet.

c) 7, 48, 50: 7^2 + 48^2 = 49 + 2304 = 2353, which is not equal to 50^2 (2500). So, this is not a Pythagorean triplet.

d) 14, 48, 50: 14^2 + 48^2 = 196 + 2304 = 2500, which is equal to 50^2 (2500). So, this is a Pythagorean triplet.

Therefore, the correct answer is d) 14, 48, 50.