Question

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

Answer 1

Hint: For the above question first of all we will have to know about the Pythagorean triplets. A Pythagorean triplet consists of three positive integers a, b, c such that ${{a}^{2}}+{{b}^{2}}={{c}^{2}}$ . Such a triplet is commonly written as (a,b,c) and a well known example is (3,4,5).

Complete step-by-step answer:
Now we have been given the first term of a Pythagorean triplet as 14. For the other two we will check the options one by one as shown below.

A. 14, 46, 52
Here, we have a=14, b=46, c=52.
\[\Rightarrow {{14}^{2}}+{{46}^{2}}=2312\ne {{52}^{2}}\]
So, this option is not correct.

B. 14, 48, 52
Here, we have a=14, b=48,c =52.
\[\Rightarrow {{14}^{2}}+{{48}^{2}}=2500\ne {{52}^{2}}\]
So, this option is not correct.

C. 14, 46, 50
Here, we have a=14, b= 46, c=50.
\[\Rightarrow {{14}^{2}}+{{46}^{2}}=2312\ne {{50}^{2}}\]
So, this option is not correct.

D. 14, 48, 50
Here, we have a=14, b= 48, c= 50.
\[\Rightarrow {{14}^{2}}+{{48}^{2}}=2500={{50}^{2}}\]
So, this is the correct option.
Therefore, the correct answer of the above question is option D.

Note: Also remember the fact about the Pythagorean triplet is that any three numbers that can constitute the numerical measure of the sides of a right angled triangle is known as Pythagorean triplet. It is always applicable in the right angled triangle. If (a,b,c) represents a pythagorean triplet then “c” is hypotenuse and a, b are either base and perpendicular of a right angled triangle.