The labelled diagram of the triangle is shown below
From the diagram,
BC is common to triangles ABC and BCD.
AC is the hypotenuse of triangle ABC and BC is the hypotenuse of triangle BCD. CD and BC are corresponding legs of triangles ABC and BCD
Thus,
CD/BC = BC/AC
5/m = m/(15 + 5)
5/m = m/20
By crossmultiplying,
m * m = 5 * 20
m^2 = 100
m = square root of 100
m = 10