Why is it difficult to find length of the hypotenuse the same way the length of the legs can be found?

bc the length of the hypotenuse is the sum of the other two legs. thats why the equation is:  a^2(hypotenuse) = b^2  + c^2 (the other two legs)

It is difficult to find length that way because you still need that extra step where are apply the Pythagorean Theorem (a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the legs), which could use a lot of useless squaring, when you could do something clever instead.

both equations and proportions are better.