Comment from JosephDoggie on the question:
Very famously, the scarecrow in the Wizard of Oz movie ($1939$) misquotes the Pythagorean Theorem.
Looking up the quote on Google gives this resource which gives this bit of info:
At the end of The Wizard of Oz, the Scarecrow receives a diploma and then immediately says, "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side."
Looking up "Isosceles triangle" on Google gives a calculator and switching what we need to solve for from "base" to "side" gives us $a=\frac P2-\frac b2$ (where $P=2a+b$) because an isosceles triangle has two sides that are equal to each other. The statement made by the Scarecrow would only be true if and only if $b=0$ (while $a$ could be equal to anything) because we have$$\sqrt a+\sqrt b=\sqrt a\implies b=0,a=c_1$$where $c_1$ is any number.