Two legs of a right triangle are equal and have length a, which is an integer. The hypotenuse of that triangle has length c, which is also an integer.

Question

anonymous · Answer

What's the question?

anonymous · Answer

is it always sometimes or never true

anonymous · Answer

Do you know the Pythagorean Theorem?

anonymous · Answer

ive heard of it

anonymous · Answer

It says that if a and b are the lengths of two legs of a right triangle and c is the length of the hypotenuse, then
$$a ^{2} + b ^{2} = c ^{2}$$

anonymous · Answer

Now if a and be are equal, this becomes
$$a ^{2} + a ^{2} = b ^{2}$$
or
2a^2 = b^2.

anonymous · Answer

Am I making sense so far?

anonymous · Answer

yes

anonymous · Answer

So...
if we take the square root of both sides, we get
$$a \sqrt{2} = b$$
Now the square root of 2 is definitely not an integer, and if you multiply the square root of 2 by an integer, you won't get another integer.
So therefore, the answer is it's never true.
Does that help?

anonymous · Answer

yes thank you very much