Hello, BG5965!

If you sketch the diagram, it's quite simple . . .

Let $\displaystyle XYZ$ be a triangle with a right angle at $\displaystyle Z.$

The midpoint $\displaystyle M$ of hypotenuse $\displaystyle XY$ is twice as far from side $\displaystyle YZ$ as it is from side $\displaystyle XZ.$

Find the length of side $\displaystyle XZ$, if $\displaystyle XY = 10$ mm Let $\displaystyle d$ = distance from $\displaystyle M$ to $\displaystyle XZ.$ Code:

X *
|\
| \
2d | \ 5
| \
| d \ M
* - - *
|\ :\
| \ : \
2d | \ : \ 5
| \ :2d \
| \: \
Z *-----*-----* Y
d d

The diagram is filled with congruent right triangles!

Using Pythagorus on $\displaystyle \Delta XYZ\!:\;\;(2d)^2 + (4d)^2 \:=\:10^2 \quad\Rightarrow\quad 4d^2 + 16d^2 \:=\:100 $

. . $\displaystyle 20d^2 \:=\:100 \quad\Rightarrow\quad d^2 \:=\:5 \quad\Rightarrow\quad d \:=\:\sqrt{5}$

Therefore: .$\displaystyle XZ \:=\:4d \;=\;4\sqrt{5}$