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

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.`

Answer 2

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 :^)