Question

Identify with reason whether the following are Pythagoras triplet 27, 70, 74.

Answer 1

Hint: A Pythagoras triplet as the name suggests consists of three numbers let them be a, b, c such that the sum of the square of any two of the numbers is equal to the square of the third number that is $ {a^2} + {b^2} = {c^2}\,or\,{a^2} + {c^2} = {b^2}\,or\,{b^2} + {c^2} = {a^2} $ , the Pythagoras triplet is derived from the Pythagoras theorem so any Pythagoras triplet also represents the sides of a right-angled triangle. Using this definition, we can find out the correct answer

Complete step-by-step answer:
The square of 27 is $ {(27)^2} = 729 $
The square of 70 is $ {(70)^2} = 4900 $
The square of 74 is $ {(74)^2} = 5476 $
Now, we see that –
 $
  729 + 4900 = 5629 \\
   \Rightarrow 5629 \ne 5476 \\
   \Rightarrow {(27)^2} + {(70)^2} \ne {(74)^2}...(1) \;
  $
 $
  729 + 5476 = 6205 \\
   \Rightarrow 6205 \ne 4900 \\
   \Rightarrow {(27)^2} + {(74)^2} \ne {(70)^2}...(1) \;
  $
 $
  4900 + 5476 = 10376 \\
   \Rightarrow 10376 \ne 729 \\
   \Rightarrow {(70)^2} + {(74)^2} \ne {(27)^2}...(3) \;
  $
From (1), (2) and (3), we observe that in the given triplet, the sum of the square of any two numbers is not equal to the square of the third number. Thus, 27, 70, 74 is not a Pythagoras triplet.
So, the correct answer is “27, 70, 74 is not a Pythagoras triplet.”.

Note: In a right-angled triangle, two sides are perpendicular to each other and are called base and height of the right-angled triangle, the line joining the endpoints of base and height is called the hypotenuse of the right-angled triangle. Pythagoras theorem tells us the relation between these three sides of the right-angled triangle, in simple terms; it states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the square of the other two sides that is the base and the height. This way, Pythagoras triplet can represent the sides of a right-angled triangle.