Question

If a = 8 and b = 6, how do you find c?

Answer 1

Hint: 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, Pythagora's triplet can represent the sides of a right-angled triangle. In this question, we are given 2 of the three numbers of a Pythagoras triplet and we have to find the third one. So, using the above information, we can find out the correct answer

Complete step-by-step solution:
According to Pythagoras theorem –
$
  {a^2} + {b^2} = {c^2} \\
   \Rightarrow {(6)^2} + {(8)^2} = {c^2} \\
   \Rightarrow {c^2} = 36 + 64 \\
   \Rightarrow {c^2} = 100 \\
   \Rightarrow c = \pm 10 \\
 $
As length cannot be negative, so the negative value is rejected.
Hence, the value of c is 10.

Note: As the name suggests, a Pythagoras triplet 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.