Question

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.

Answer 1

What's the question?

Answer 2

is it always sometimes or never true

Answer 3

Do you know the Pythagorean Theorem?

Answer 4

ive heard of it

Answer 5

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
\[a ^{2} + b ^{2} = c ^{2}\]

Answer 6

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

Answer 7

Am I making sense so far?

Answer 8

yes

Answer 9

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?

Answer 10

yes thank you very much