pythagorean theorem

Question

Suppose you are given a right triangle with hypotenuse of length r and legs of length x−0.5 and x+0.5.

Determine formulas (based upon ) for the lengths of the two legs.

Shorter leg

Longer leg

Answer 1

Short leg:

x - 0.5 = √[r² - (x + 0.5)²]

Long leg:

x + 0.5 = √[r² - (x - 0.5)²]