(Q1)For a right angled triangle with integer sides atleast one of its measurements must be an even number. Why? Discuss this with your friends and teachers.

Solution :

Let l, m, n are integer sides of a angled triangle.

then l² = m² + n²

⇒ n² = l² - m² = (l + m) (l - m)

Now,

Case I :

 Both l,m are even the (l + m) is even then (l + m) (l - m) is also even. So 'n' is even. Here all are .

Case II :

 Both l, m are odd then (l + m) and (l - m) become even. Then the product of even numbers is even so 'n' is .

 Here only 'n' is .

Case III :

 If we consider l is even, m is' odd then 'n' will be odd. So here T is even. We observe in all above three cases at least one of l, m, n is ;

 Hence Proved