Question

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the

Answer 1

Answer:

For the value of hypotenuse can be irrational, sum of squares of other two legs might be imperfect square number.

Step-by-step explanation:

We all know, the Pythagorean theorem can be stated as follows:

The sum of squares of two legs of a right angled triangle is equal to the square of the hypotenuse.

i.e.

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

Where, $c$ is the hypotenuse and $a, b$ are the two other legs of the right angled triangle.

Given that:

$a$ and $b$ are rational numbers.

To find:

Situation for which $c$ is irrational.

Square of a rational number is always rational.

So, $a^{2} , b^{2}$ both will be rational.

And sum of squares of two rational numbers will also be rational.

Therefore, $a^2+b^2$ will also be rational.

and

$c = \sqrt{a^2+b^2}$

For the value of $c$ can be irrational, sum of squares of other two legs might be imperfect square number.