Question

24 and 32 are the given lengths of a right triangle with the unknown length (x) being 40, how do I tell if its a leg or the hypotenuse?

Answer 1

By the Pythagorean theorem

$a^2=b^2+c^2$⇒

$40^2=24^2+32^2\\1600=1600$

So a triangle with these sides exists

In a right triangle, the largest side is a hypotenuse, so the side with length 40 is a hypotenuse.

P.S. Hello from Russia and sorry for my bad english :^)

Answer 2

Step-by-step explanation:

If the sum of the squares of 24 and 32 are equal to square of 40, then it is a hypotenuse.

Let us check.

${24}^{2} + {32}^{2} = 576 + 1024 = 1600...(1) \\ {40}^{2} = 1600...(2) \\ from \: equations \: (1) \: and \: (2) \\ {24}^{2} + {32}^{2} = {40}^{2} \\ \therefore \: 24 \: and \: 32 \: are \: lengths \: of \: legs \\ and \: 40 \: is \: the \: length \: of \: hypotenuse.$