If the smallest number in a Pythagorean triplet is 14, find the other two numbers.A. 14, 46, 52B. 14, 48, 52C. 14, 46, 50D. 14, 48, 50

A Pythagorean triplet consists of three positive integers a, b, and c that satisfy the equation a² + b² = c². The number 14 is given as the smallest number in the triplet, which means a = 14. We need to find the other two numbers, b and c.

To solve this, we will use the Pythagorean theorem a² + b² = c² and try different values for b and c that satisfy the equation.

Given: a = 14

The equation becomes: 14² + b² = c²

First, calculate 14²: 14² = 196
So, the equation becomes: 196 + b² = c²

Now, let's check the possible values for b and c from the options:
Option A: 14, 46, 52

Check: 14² + 46² = 52²
196 + 2116 = 2704
2312 ≠ 2704, so this is not a valid triplet.
Option B: 14, 48, 52

Check: 14² + 48² = 52²
196 + 2304 = 2704
2500 ≠ 2704, so this is not a valid triplet.
Option C: 14, 46, 50

Check: 14² + 46² = 50²
196 + 2116 = 2500
2312 ≠ 2500, so this is not a valid triplet.
Option D: 14, 48, 50

Check: 14² + 48² = 50²
196 + 2304 = 2500
2500 = 2500, which is true.
Thus, the correct Pythagorean triplet is 14, 48, and 50.

Answer: D. 14, 48, 50