Question

find the given number are pythagorean tripletnor not 6,9,12​

Answer 1

Solution:

Let us assume that 6,9 and 12 are sides of a right angled triangle. The largest side (Hypotenuse) can be taken as the largest value and the other values can be considered as the altitude and height respectively. The formula to be implemented here is the Pythagoras theorem:

$\sf{\implies\:Hypotenuse^2=Altitude^2+Base^2}$

Here, let's assume the values as:

✳ Hypotenuse = 12 cm

✳ Altitude = 9 cm

✳ Base = 6 cm

Substituting the values into the equation in LHS and RHS:

LHS:

$\sf{=Hypotenuse^2}$

$\sf{=12^2}$

$\sf{=144}$

RHS:

$\sf{=Altitude^2+Base^2}$

$\sf{=9^2+6^2}$

$\sf{=81+36}$

$\sf{=117}$

$\bf{LHS\neq\:RHS}$

As, the LHS is not equal to the RHS, these measures are not values of a right angled triangle and henceforth they do not form a Pythagorean triplet.

Pythagorean triplet:

Three positive integers that are capable of forming a right angled triangle and is applicable in the Pythagoras theorem is known as a Pythagorean triplet.

(3, 4, 5) and (7, 24, 25) form a Pythagorean triplet.