Question

The legs of a rt. triangle are 6cm and 8cm. What is the length of the median to the hypotenuse?

Answer 1

The median has length five. An intuitive way to argue this is to look at the right triangle as half of a rectangle with length 6, width 8, and a diagonal, of course, of 10.
(I will draw a diagram.) The two diagonals of a rectangle are congruent and also bisect each other. Hence, what is a median to the hypotenuse of the original right triangle is half a diagonal of the rectangle and has length 5.