What happens to the hypotenuse of a right triangle if you double the length of the legs of the triangle?

Answer 1

If you double the lengths of the legs of a right triangle, the lengths of the new legs become 2a and 2b (if the original legs are a and b). According to the Pythagorean theorem, the hypotenuse (c) of the original triangle is given by (c = \sqrt{a^2 + b^2}). When you double the legs, the new hypotenuse becomes (c' = \sqrt{(2a)^2 + (2b)^2} = \sqrt{4a^2 + 4b^2} = 2\sqrt{a^2 + b^2} = 2c). Therefore, the hypotenuse also doubles in length.