Question

For a right angled triangle with integer sides atleast one of its measurements must be an even number.Why?

Answer 1

Answer:

A right angled triangle follows Pythagoras theorem. means to say if a , b , c are the sides of right angled triangle then, it should be

a^2=b^2+c^2\\or,b^2=c^2+a^2\\or,c^2=a^2+b^2

for a² = b² + c² , a is known as hypotenuse.

if we assume a is an odd number then a² must be an odd number .

Let a² = k

similarly, we can assume b is an odd number

then, b² must be an odd number .

Let b² = m

now, k = c² + m

we see k is an odd number is sum of two different number in which one is also an odd number.e.g., m . then c² should be an even number. because sum of two odd number is always even number . hence for getting odd number of sum of two different number in which one is odd then other must be even number.

hence, c² is an even number . so, c must be an even number.

therefore, For a right angled triangle with integer sides atleast one of its measurements must be an even number.

Answer 2

Answer:

multiple of 2,.

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