Question

Write statement of Pythagoras theorem and show that the $6,8$ and $10$ are Pythagorean triplets.

Answer 1

Pythagoras Theorem: In a right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares of its remaining two sides.

$(Hypotenuse{)}^2=(Perpendicular{)}^2+(Base{)}^2$

$(AC{)}^2=(CB{)}^2+(BA{)}^2$

For Pythagorean triplets:

$a^2+b^2=c^2$

$a=6$

$b=8$

$c=10$

$\therefore 6^2+8^2=36+64=100={10}^2$

That is $a^2+b^2=c^2$

Hence $6,8,10$ are Pythagorean triplets.