Question

Find the Pythagorean triplet in which one member is 12.
A. 5,12,13
B. 7,12,19
C. 11,12,15
D. 11,12,18

Answer 1

Hint- In order to find the Pythagorean triplet, find the set of numbers amongst the given options which satisfies the Pythagoras theorem.

Complete step-by-step solution -
Pythagoras theorem states that
${\text{hypotenus}}{{\text{e}}^2} = {\text{bas}}{{\text{e}}^2} + {\text{perpendicula}}{{\text{r}}^2}$
The option which satisfies this property is the correct option.
Checking option ‘A’
$
  \therefore {13^2} = {5^2} + {12^2} \\
  169 = 25 + 144 \\
  169 = 169 \\
$
Hence, it is a Pythagorean triplet.
Checking option ‘B’
$
  {19^2} = {12^2} + {7^2} \\
  361 = 144 + 49 \\
  361 \ne 293 \\
 $
Therefore, it cannot be the correct option
Checking option ‘C’
$
  {15^2} = {11^2} + {12^2} \\
  225 = 121 + 144 \\
  225 \ne 265 \\
$
Therefore, it is also not the correct option.
Checking option ‘D’
$
  {18^2} = {11^2} + {12^2} \\
  324 = 121 + 144 \\
  324 \ne 265 \\
$
Therefore, it is also the wrong option.

Hence, the correct option is A.

Note- Pythagorean triplet is that set of numbers which follows the Pythagoras Theorem which states that, in a right-angled triangle the square of hypotenuse is equal to the sum of squares of other two sides. Some basic Pythagorean triplets like 5,12,13 must be remembered by students.