As below,
I know how to find the length. but how to prove?
thanks.
Three line segments, of lengths a, b, and c, can form a triangle as long as no one length is greater than the sum of the other two (the shortest distance between two points is a straight line). But if $\displaystyle c^2= a^2+ b^2$ it is certainly true that the longest side is c and c< a+ b. A right triangle is a triangle as Plato said.
(To see that $\displaystyle c^2= a^2+ b^2$ leads to $\displaystyle c< a+ b$ [as long as neither of a or b is 0], add the positive number 2ab to both sides of $\displaystyle c^2= a^2+ b^2$. You get $\displaystyle c^2+ 2ab= a^2+ 2ab+ b^2= (a+ b)^2$. Since $\displaystyle (a+ b)^2$ is larger than $\displaystyle c^2$, a+ b is larger than c.)