Question

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

Answer 1

Pythagoras Theorem

1. Pythagoras Theorem states that the square of the longest side of a right triangle is equal to the sum of the squares of other two sides.
2. The sides of the right triangle or the sides of triangle which follow Pythagoras theorem are known as Pythagorean Triplets.
3. If $h$ is the hypotenuse, $b$ is the base and $l$ is the height of the right angle triangle then $h^2=b^2+l^2$

Here given sides of the right triangle are $6,8$ and $10$, in which longest side is $10$.

So, if the given sides are the Pythagorean triples then they must follow Pythagoras Theorem ,i.e.,

Square of hypotenuse (longest side of right angles triangle) $=$ Sum of the square of the other two sides of the triangle.

Now, square of $10$ is${10}^2=100$

And sum of the squares of other two sides are

$6^2+8^2=36+64$

$\Rightarrow$ $=100$

$\Rightarrow$ $={10}^2$

Thus the given sides follow Pythagoras Theorem.

Hence, the given sides are Pythagorean Triplets.